Física – investigación de Nahual Sobrino Coll

2026

1. Thermodynamic bound on the Fano factor of a coherent thermoelectric heat engine
   Nahual Sobrino, Rosario Fazio, Matteo Acciai
   Preprint
   arXiv:2607.11704PDF

   Resumen

   We show that for fermionic coherent thermoelectric transport, selecting heat-engine operation yields a thermodynamic uncertainty relation for the charge current that imposes a universal lower limit of $F > 1/2$ on the corresponding Fano factor. We find that violations of the thermodynamic uncertainty relation for classical Markov processes, typically associated with a quantum advantage, are far more restricted for heat engines than what is allowed by a generic thermodynamic process. For bosonic and classical carriers, the minimum Fano factor increases to $F > 1$, and the thermodynamic uncertainty relation for classical Markov processes is never violated. We provide numerical evidence that all the obtained bounds are tight and can be saturated by properly designed transmissions.

   BibTeX

   @misc{Sobrino2026thermodynamic,
     title         = {{Thermodynamic bound on the Fano factor of a coherent thermoelectric heat engine}},
     author        = {Nahual Sobrino and Rosario Fazio and Matteo Acciai},
     year          = {2026},
     eprint        = {2607.11704},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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2. Spectral and transmission properties of multiple correlated quantum dots made simple
   Nahual Sobrino, Stefan Kurth
   Preprint
   arXiv:2605.20083PDF

   Resumen

   Steady-state density functional theory, called i-DFT, is employed to compute spectral and transmission properties of general interacting nanoscale regions coupled to electronic reservoirs. Exchange-correlation functionals are constructed for different interactions and coupling geometries. The potential of the method is illustrated by applications to various multiple quantum dots from the Coulomb blockade to the Kondo regime, capturing phenomena such as quantum phase transitions. The results are in excellent agreement with many-body approaches at a fraction of the computational cost.

   BibTeX

   @misc{Sobrino2026spectral,
     title         = {{Spectral and transmission properties of multiple correlated quantum dots made simple}},
     author        = {Nahual Sobrino and Stefan Kurth},
     year          = {2026},
     eprint        = {2605.20083},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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3. Current precision in interacting hybrid Normal-Superconducting systems
   Nahual Sobrino, Fabio Taddei, Rosario Fazio, Michele Governale
   Phys. Rev. B 113, 195407 (2026)
   arXiv:2602.06781PDFDOI

   Resumen

   We study Andreev-mediated transport and current fluctuations in interacting normal-superconducting quantum-dot systems. Using a generalized master equation based on real-time diagrammatics and full counting statistics, we compute the steady-state current, zero-frequency noise, and rate of entropy production in the large superconducting-gap limit. We show how Coulomb interactions modify Andreev-mediated transport by renormalizing resonant conditions and suppressing superconducting coherence, leading to a pronounced reduction of current precision even when average currents are only weakly affected. These effects are particularly evident at high temperatures, where conventional Coulomb-blockade features are thermally smeared while fluctuation properties remain highly sensitive. By analyzing thermodynamic uncertainty relations, we demonstrate that violations of the quantum bound present in the noninteracting regime are progressively reduced and eventually suppressed as interactions increase, whereas the recently proposed hybrid bound remains satisfied. Our results clarify how Coulomb interactions, and nonequilibrium fluctuations jointly determine transport properties in hybrid superconducting devices, and establish current precision as a robust benchmark for interacting Andreev transport beyond the noninteracting limit.

   BibTeX

   @article{Sobrino2026current,
     title         = {{Current precision in interacting hybrid Normal-Superconducting systems}},
     author        = {Nahual Sobrino and Fabio Taddei and Rosario Fazio and Michele Governale},
     journal       = {Phys. Rev. B},
     volume        = {113},
     pages         = {195407},
     year          = {2026},
     doi           = {10.1103/g1z3-m73v},
     eprint        = {2602.06781},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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4. Quantum thermodynamic uncertainty relation and macroscopic superconducting coherence
   Franco Mayo, Nahual Sobrino, Rosario Fazio, Fabio Taddei, Michele Governale
   Phys. Rev. Research 8, 013242 (2026)
   arXiv:2506.02904PDFDOI

   Resumen

   Stability and efficiency are mutually exclusive in a thermodynamic process, e.g. in a thermal machine. Any effort to reduce the fluctuations of a certain output quantity is necessarily accompanied by an increase of entropy production, therefore lowering its efficiency. This interplay is beautifully captured by the so called Thermodynamic Uncertainty Relations (TURs) which set a lower bound on the relative uncertainty of a current for a given rate of entropy production. Their status in hybrid normal-superconducting (N-S) devices has remained unsettled. We show that, in the subgap regime, departures from the normal quantum TUR are governed by {\it macroscopic} superconducting coherence quantified by the pair amplitude, and that introducing a dephasing probe suppresses this coherence and restores the bound. We further derive a hybrid quantum TUR that is general for two-terminal N-S junctions in the Andreev regime: the inequality is never violated, is saturated only at vanishing current, and is related to the normal quantum bound under the replacement (e to 2e). For N-S quantum dot and Cooper-pair-splitter systems we compute current and noise and show that deviations from the normal bound track the pair amplitude on the central region. The results establish a direct link between superconducting macroscopic coherence and nonequilibrium fluctuations and supply a general bound for the Andreev regime.

   BibTeX

   @article{Mayo2026quantum,
     title         = {{Quantum thermodynamic uncertainty relation and macroscopic superconducting coherence}},
     author        = {Franco Mayo and Nahual Sobrino and Rosario Fazio and Fabio Taddei and Michele Governale},
     journal       = {Phys. Rev. Research},
     volume        = {8},
     pages         = {013242},
     year          = {2026},
     doi           = {10.1103/tfsv-fjzd},
     eprint        = {2506.02904},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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5. A Useful Metric for the NISQ Era: Qubit Error Probability and Its Role in Zero Noise Extrapolation
   Nahual Sobrino, Unai Aseginolaza, Joaquim Jornet-Somoza, Juan Borge
   AVS Quantum Sci. 8, 013803 (2026)
   arXiv:2503.10204PDFDOI

   Resumen

   Accurate assessment and management of errors is indispensable for extracting useful results from noisy intermediate-scale quantum (NISQ) devices. In this work, we propose the qubit error probability (QEP), a device specific metric that combines relaxation, dephasing, gate, and measurement contributions into a single per qubit figure of merit computable before execution. Leveraging QEP as the control variable, we revisit zero noise extrapolation (ZNE) by adding pairs of controlled native two-qubit gates on all connected qubit pairs to generate circuits with successively larger mean QEP; the zero error limit is then approximated by a linear regression of the measured observable against those values. Benchmarking on IBM Quantum Heron processors, we apply QEP guided ZNE to first order Trotterized simulations of the two dimensional transverse field Ising model, chosen as a representative interacting many body system, involving up to 68 qubits and 15 Trotter steps. In regimes where the raw circuits exhibit a finite mean QEP, the method suppresses observable errors beyond those attainable with circuit depth scaled ZNE, while requiring only three noise scaled evaluations and no additional classical post processing. These results demonstrate that QEP serves as a transparent and efficient error metric, and that its integration into ZNE provides a practical route to reliability gains on current superconducting hardware, without the resource costs associated with full quantum error correction.

   BibTeX

   @article{Sobrino2026useful,
     title         = {{A Useful Metric for the NISQ Era: Qubit Error Probability and Its Role in Zero Noise Extrapolation}},
     author        = {Nahual Sobrino and Unai Aseginolaza and Joaquim Jornet-Somoza and Juan Borge},
     journal       = {AVS Quantum Sci.},
     volume        = {8},
     pages         = {013803},
     year          = {2026},
     doi           = {10.1116/5.0287324},
     eprint        = {2503.10204},
     archivePrefix = {arXiv},
     primaryClass  = {quant-ph}
   }

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2025

1. Thermoelectric properties of interacting double quantum dots
   Nahual Sobrino
   Phys. Rev. B 112, 235101 (2025)
   arXiv:2510.20397PDFDOI

   Resumen

   We investigate the thermoelectric transport properties of an interacting parallel double quantum dot in the Coulomb-blockade regime. Building on an analytical solution based on an equation-of-motion technique, we extend the formalism for the asymmetrically coupled situation and provide compact closed-form expressions for steady-state currents together with the differential conductance, Seebeck coefficient, and thermal conductance. We determine the operating points that maximize efficiency and output power of the system, clarifying their relation to standard near-equilibrium ZT expressions. We further study the thermal rectification in both the open- and closed-circuit configurations and derive an expression for the open-circuit case. Interaction-induced resonances are understood in terms of the poles of the resulting Green's function, generating gate and bias dependent regions of enhanced efficiency at finite power, negative differential thermal conductance, and finite thermal rectification.

   BibTeX

   @article{Sobrino2025thermoelectric,
     title         = {{Thermoelectric properties of interacting double quantum dots}},
     author        = {Nahual Sobrino},
     journal       = {Phys. Rev. B},
     volume        = {112},
     pages         = {235101},
     year          = {2025},
     doi           = {10.1103/c8pl-h1jh},
     eprint        = {2510.20397},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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2. Analytic approach to thermoelectric transport in double quantum dots
   Nahual Sobrino, David Jacob, Stefan Kurth
   Phys. Rev. B 111, 115108 (2025)
   arXiv:2409.17064PDFDOI

   Resumen

   A recently proposed analytical solution for the equations of motion of the one-body Green function of the double quantum dot is extended to the out-of-equilibrium situation. By solving a linear system for the density correlators, not only the local occupations but also charge and heat currents as well as transport coefficients and the figure of merit are analytically derived in terms of system parameters and external driving forces. The emerging regions of stable occupation and finite currents are explained in terms of addition and removal energies, corresponding to the poles of the Green function. The analytical results are validated against the hierarchical equations of motion method, showing excellent agreement.

   BibTeX

   @article{Sobrino2025analytic,
     title         = {{Analytic approach to thermoelectric transport in double quantum dots}},
     author        = {Nahual Sobrino and David Jacob and Stefan Kurth},
     journal       = {Phys. Rev. B},
     volume        = {111},
     pages         = {115108},
     year          = {2025},
     doi           = {10.1103/PhysRevB.111.115108},
     eprint        = {2409.17064},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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2024

1. Fully analytical equation of motion approach for the double quantum dot in the Coulomb blockade regime
   Nahual Sobrino, David Jacob, Stefan Kurth
   Phys. Rev. B 110, 115121 (2024)
   arXiv:2406.19357PDFDOI

   Resumen

   A fully analytical approach based on the equation of motion technique to investigate the spectral properties and orbital occupations in an interacting double quantum dot in equilibrium is presented. By solving a linear system for the density correlators analytically, an explicit expression for the one body Green's function in terms of local occupations, intra- and inter-dot Coulomb interactions, and the model parameters is derived. In the uncontacted limit, the results coincide with those obtained from the grand canonical ensemble. The analytical results compare favourably with numerical results obtained with the non-crossing approximation and the hierarchical equation of motion methods accurately reproducing peak positions and spectral weight distributions in the Coulomb blockade regime.

   BibTeX

   @article{Sobrino2024fully,
     title         = {{Fully analytical equation of motion approach for the double quantum dot in the Coulomb blockade regime}},
     author        = {Nahual Sobrino and David Jacob and Stefan Kurth},
     journal       = {Phys. Rev. B},
     volume        = {110},
     pages         = {115121},
     year          = {2024},
     doi           = {10.1103/PhysRevB.110.115121},
     eprint        = {2406.19357},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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2. Demonstrating Kondo behavior by temperature-dependent scanning tunneling spectroscopy
   Elia Turco, Markus Aapro, Somesh C. Ganguli, Nils Krane, Robert Drost, …, Nahual Sobrino et al. (12 autores)
   Phys. Rev. Research 6, L022061 (2024)
   arXiv:2310.09326PDFDOI

   Resumen

   The Kondo effect describes the scattering of conduction electrons by magnetic impurities, manifesting as an electronic resonance at the Fermi energy with a distinctive temperature evolution. In this letter, we present a critical evaluation of the current methodology employed to demonstrate Kondo behavior in transport measurements, underscoring the limitations of established theoretical frameworks and the influence of extrinsic broadening. We introduce a novel approach for analyzing spectroscopic indicators of the Kondo effect, employing the Hurwitz-Fano lineshape as a model for the Kondo resonance in the presence of extrinsic broadening. Through precise scanning tunneling spectroscopy measurements on an exemplary spin-1/2 Kondo system, phenalenyl on Au(111), we demonstrate the efficacy of our proposed protocol in extracting accurate intrinsic Kondo linewidths from finite-temperature measurements. The extracted linewidths exhibit a robust fit with a recently derived expression for the temperature-dependent intrinsic Kondo linewidth, providing compelling evidence for the validity of the underlying theory.

   BibTeX

   @article{Turco2024demonstrating,
     title         = {{Demonstrating Kondo behavior by temperature-dependent scanning tunneling spectroscopy}},
     author        = {Elia Turco and Markus Aapro and Somesh C. Ganguli and Nils Krane and Robert Drost and Nahual Sobrino and Annika Bernhardt and Michal Juríček and Roman Fasel and Pascal Ruffieux and Peter Liljeroth and David Jacob},
     journal       = {Phys. Rev. Research},
     volume        = {6},
     pages         = {L022061},
     year          = {2024},
     doi           = {10.1103/PhysRevResearch.6.L022061},
     eprint        = {2310.09326},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.str-el}
   }

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3. Error estimation in current noisy quantum computers
   Unai Aseguinolaza, Nahual Sobrino, Gabriel Sobrino, Joaquim Jornet-Somoza, Juan Borge
   Quantum Inf. Process. 23, 181 (2024)
   arXiv:2302.06870PDFDOI

   Resumen

   One of the main important features of the noisy intermediate-scale quantum (NISQ) era is the correct evaluation and consideration of errors. In this paper, we analyze the main sources of errors in current (IBM) quantum computers and we present a useful tool (TED-qc) designed to facilitate the total error probability expected for any quantum circuit. We propose this total error probability as the best way to estimate a lower bound for the fidelity in the NISQ era, avoiding the necessity of comparing the quantum calculations with any classical one. In order to contrast the robustness of our tool we compute the total error probability that may occur in three different quantum models: 1) the Ising model, 2) the Quantum-Phase Estimation (QPE), and 3) the Grover's algorithm. For each model, the main quantities of interest are computed and benchmarked against the reference simulator's results as a function of the error probability for a representative and statistically significant sample size. The analysis is satisfactory in more than the $99\%$ of the cases. In addition, we study how error mitigation techniques are able to eliminate the noise induced during the measurement. These results have been calculated for the IBM quantum computers, but both the tool and the analysis can be easily extended to any other quantum computer.

   BibTeX

   @article{Aseguinolaza2024error,
     title         = {{Error estimation in current noisy quantum computers}},
     author        = {Unai Aseguinolaza and Nahual Sobrino and Gabriel Sobrino and Joaquim Jornet-Somoza and Juan Borge},
     journal       = {Quantum Inf. Process.},
     volume        = {23},
     pages         = {181},
     year          = {2024},
     doi           = {10.1007/s11128-024-04384-z},
     eprint        = {2302.06870},
     archivePrefix = {arXiv},
     primaryClass  = {quant-ph}
   }

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2023

1. What can lattice DFT teach us about real-space DFT?
   Nahual Sobrino, David Jacob, Stefan Kurth
   J. Chem. Phys. 159, 154110 (2023)
   arXiv:2308.01185PDFDOI

   Resumen

   In this paper we establish a connection between density functional theory (DFT) for lattice models and common real-space DFT. We consider the lattice DFT description of a two-level model subject to generic interactions in Mermin's DFT formulation in the grand canonical ensemble at finite temperature. The case of only density-density and Hund's rule interaction studied in earlier work is shown to be equivalent to an exact-exchange description of DFT in the real-space picture. In addition, we also include the so-called pair-hopping interaction which can be treated analytically and, crucially, leads to non-integer occupations of the Kohn-Sham levels even in the limit of zero temperature. Treating the hydrogen molecule in a minimal basis is shown to be equivalent to our two-level lattice DFT model. By means of the fractional occupations of the KS orbitals (which, in this case, are identical to the many-body ones) we reproduce the results of full configuration interaction, even in the dissociation limit and without breaking the spin symmetry. Beyond the minimal basis, we embed our HOMO-LUMO model into a standard DFT calculation and, again, obtain results in overall good agreement with exact ones without the need of breaking the spin symmetry.

   BibTeX

   @article{Sobrino2023what,
     title         = {{What can lattice DFT teach us about real-space DFT?}},
     author        = {Nahual Sobrino and David Jacob and Stefan Kurth},
     journal       = {J. Chem. Phys.},
     volume        = {159},
     pages         = {154110},
     year          = {2023},
     doi           = {10.1063/5.0170312},
     eprint        = {2308.01185},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.str-el}
   }

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2. Thermoelectric efficiency in multiterminal quantum thermal machines from steady-state density functional theory
   Nahual Sobrino, Roberto D'Agosta, Stefan Kurth
   Phys. Rev. B 107, 195116 (2023)
   arXiv:2303.01355PDFDOI

   Resumen

   The multi-terminal generalization of the steady-state density functional theory for the description of electronic and thermal transport (iq-DFT) is presented. The linear response regime of the framework is developed leading to exact expressions for the many-body transport coefficients and thermoelectric efficiency purely in terms of quantities accessible to the framework. The theory is applied to a multi-terminal interacting quantum dot in the Coulomb blockade regime for which accurate parametrizations of the exchange-correlation kernel matrix are given. The thermoelectric efficiency and output power of the multi-terminal system are studied. Surprisingly, the strong-interaction limit of these quantities can be understood in terms of the non-interacting one.

   BibTeX

   @article{Sobrino2023thermoelectric,
     title         = {{Thermoelectric efficiency in multiterminal quantum thermal machines from steady-state density functional theory}},
     author        = {Nahual Sobrino and Roberto D'Agosta and Stefan Kurth},
     journal       = {Phys. Rev. B},
     volume        = {107},
     pages         = {195116},
     year          = {2023},
     doi           = {10.1103/PhysRevB.107.195116},
     eprint        = {2303.01355},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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3. Parameter and $q$ asymptotics of $\mathfrak{L}_{q}$-norms of hypergeometric orthogonal polynomials
   Nahual Sobrino, J. S. Dehesa
   Int. J. Quantum Chem. 123, e27013 (2023)
   arXiv:2204.11242PDFDOI

   Resumen

   The three canonical families of the hypergeometric orthogonal polynomials (Hermite, Laguerre and Jacobi) control the physical wavefunctions of the bound stationary states of a great deal of quantum systems. The algebraic $\mathfrak{L}_{q}$-norms of these polynomials describe many physical, chemical and information-theoretical properties of these systems, such as e.g. the kinetic and Weizsäcker energies, the position and momentum expectation values, the Rényi and Shannon entropies and the Cramér-Rao, the Fisher-Shannon and LMC measures of complexity. In this work we examine, partially review and solve the $q$-asymptotics and the parameter asymptotics (i.e., when the weight function's parameter tends towards infinity) of the unweighted and weighted $\mathfrak{L}_{q}$-norms for these orthogonal polynomials. This study has been motivated by the application of these algebraic norms to the energetic, entropic and complexity-like properties of the highly-excited Rydberg and high-dimensional pseudo-classical states of harmonic (oscillator-like) and Coulomb (hydrogenic) systems, and other quantum systems subject to central potentials of anharmonic type.

   BibTeX

   @article{Sobrino2023parameter,
     title         = {{Parameter and $q$ asymptotics of $\mathfrak{L}_{q}$-norms of hypergeometric orthogonal polynomials}},
     author        = {Nahual Sobrino and J. S. Dehesa},
     journal       = {Int. J. Quantum Chem.},
     volume        = {123},
     pages         = {e27013},
     year          = {2023},
     doi           = {10.1002/qua.27013},
     eprint        = {2204.11242},
     archivePrefix = {arXiv},
     primaryClass  = {math-ph}
   }

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2022

1. Level occupation switching with density functional theory
   Nahual Sobrino, David Jacob, Stefan Kurth
   Phys. Rev. B 106, 195124 (2022)
   arXiv:2209.06754PDFDOI

   Resumen

   The charge transport properties of zero-temperature multi-orbital quantum dot systems with one dot coupled to leads and the other dots coupled only capacitatively are studied within density functional theory. It is shown that the setup is equivalent to an effective single impurity Anderson model. This allows to understand the level occupation switching effect as transitions between ground states of different integer occupations in the uncoupled dots. Level occupation switching is very sensitive to small energy differences and therefore also to the details of the parametrized exchange-correlation functionals. An existing functional already captures the effect on a qualitative level but we also provide an improved parametrization which is very accurate when compared to reference numerical renormalization group results.

   BibTeX

   @article{Sobrino2022level,
     title         = {{Level occupation switching with density functional theory}},
     author        = {Nahual Sobrino and David Jacob and Stefan Kurth},
     journal       = {Phys. Rev. B},
     volume        = {106},
     pages         = {195124},
     year          = {2022},
     doi           = {10.1103/PhysRevB.106.195124},
     eprint        = {2209.06754},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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2021

1. Algebraic $\mathcal{L}_{q}$-norms and complexity-like properties of Jacobi polynomials-Degree and parameter asymptotics
   Nahual Sobrino, Jesus S. Dehesa
   Int. J. Quantum Chem. 122, e26858 (2021)
   arXiv:2110.11441PDFDOI

   Resumen

   The Jacobi polynomials $\hat{P}_n^{(α,β)}(x)$ conform the canonical family of hypergeometric orthogonal polynomials (HOPs) with the two-parameter weight function $(1-x)^α(1+x)^β, α,β>-1,$ on the interval $[-1,+1]$. The spreading of its associated probability density (i.e., the Rakhmanov density) over the orthogonality support has been quantified, beyond the dispersion measures (moments around the origin, variance), by the algebraic $\mathfrak{L}_{q}$-norms (Shannon and Rényi entropies) and the monotonic complexity-like measures of Cramér-Rao, Fisher-Shannon and LMC (López-Ruiz, Mancini and Calbet) types. These quantities, however, have been often determined in an analytically highbrow, non-handy way; specially when the degree or the parameters $(α,β)$ are large. In this work, we determine in a simple, compact form the entropic and complexity-like properties of the Jacobi polynomials in the two extremal situations: ($n\rightarrow \infty$; fixed $α,β$) and ($α\rightarrow \infty$; fixed $n,β$). These two asymptotics are relevant \textit{per se} and because they control the physical entropy and complexity measures of the high energy (Rydberg) and high dimensional (pseudoclassical) states of numerous supersymmetric quantum-mechanical systems.

   BibTeX

   @article{Sobrino2021algebraic,
     title         = {{Algebraic $\mathcal{L}_{q}$-norms and complexity-like properties of Jacobi polynomials-Degree and parameter asymptotics}},
     author        = {Nahual Sobrino and Jesus S. Dehesa},
     journal       = {Int. J. Quantum Chem.},
     volume        = {122},
     pages         = {e26858},
     year          = {2021},
     doi           = {10.1002/qua.26858},
     eprint        = {2110.11441},
     archivePrefix = {arXiv},
     primaryClass  = {math-ph}
   }

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2. Complexity-like properties and parameter asymptotics of $\mathfrak{L}_{q}$-norms of Laguerre and Gegenbauer polynomials
   Jesús S. Dehesa, Nahual Sobrino
   J. Phys. A: Math. Theor. 54, 495001 (2021)
   arXiv:2108.07214PDFDOI

   Resumen

   The main monotonic statistical complexity-like measures of the Rakhmanov's probability density associated to the hypergeometric orthogonal polynomials (HOPs) in a real continuous variable, each of them quantifying two configurational facets of spreading, are examined in this work beyond the Cramér-Rao one. The Fisher-Shannon and LMC (López-Ruiz-Mancini-Calvet) complexity measures, which have two entropic components, are analytically expressed in terms of the degree and the orthogonality weight's parameter(s) of the polynomials. The degree and parameter asymptotics of these two-fold spreading measures are shown for the parameter-dependent families of HOPs of Laguerre and Gegenbauer types. This is done by using the asymptotics of the Rényi and Shannon entropies, which are closely connected to the $\mathfrak{L}_{q}$-norms of these polynomials, when the weight's parameter tends towards infinity. The degree and parameter asymptotics of these Laguerre and Gegenbauer algebraic norms control the radial and angular charge and momentum distributions of numerous relevant multidimensional physical systems with a spherically-symmetric quantum-mechanical potential in the high-energy (Rydberg) and high-dimensional (quasi-classical) states, respectively. This is because the corresponding states' wavefunctions are expressed by means of the Laguerre and Gegenbauer polynomials in both position and momentum spaces.

   BibTeX

   @article{Dehesa2021complexity,
     title         = {{Complexity-like properties and parameter asymptotics of $\mathfrak{L}_{q}$-norms of Laguerre and Gegenbauer polynomials}},
     author        = {Jesús S. Dehesa and Nahual Sobrino},
     journal       = {J. Phys. A: Math. Theor.},
     volume        = {54},
     pages         = {495001},
     year          = {2021},
     doi           = {10.1088/1751-8121/ac3320},
     eprint        = {2108.07214},
     archivePrefix = {arXiv},
     primaryClass  = {math-ph}
   }

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3. Thermoelectric transport within density functional theory
   Nahual Sobrino, Florian Eich, Gianluca Stefanucci, Roberto D'Agosta, Stefan Kurth
   Phys. Rev. B 104, 125115 (2021)
   arXiv:2107.01940PDFDOI

   Resumen

   A new formalism to describe steady-state electronic and thermal transport in the framework of density functional theory is presented. A one-to-one correspondence is proven between the three basic variables of the theory, i.e., the density on as well as the electrical and heat currents through the junction, and the three basic potentials, i.e., the local potential in as well as the DC bias and thermal gradient across the junction. Consequently, the Kohn-Sham system of the theory requires three exchange-correlations potentials. In linear response, the new formalism leads to exact expressions for the many-body transport coefficients (both electrical and thermal conductances and Seebeck coefficient) in terms of both the corresponding Kohn-Sham coefficients and derivatives of the exchange-correlations potentials. The theory is applied to the Single Impurity Anderson Model, and an accurate analytic parametrization for these derivatives in the Coulomb blockade regime is constructed through reverse engineering.

   BibTeX

   @article{Sobrino2021thermoelectric,
     title         = {{Thermoelectric transport within density functional theory}},
     author        = {Nahual Sobrino and Florian Eich and Gianluca Stefanucci and Roberto D'Agosta and Stefan Kurth},
     journal       = {Phys. Rev. B},
     volume        = {104},
     pages         = {125115},
     year          = {2021},
     doi           = {10.1103/PhysRevB.104.125115},
     eprint        = {2107.01940},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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2020

1. Exchange-correlation potentials for multi-orbital quantum dots subject to generic density-density interactions and Hund's rule coupling
   Nahual Sobrino, Stefan Kurth, David Jacob
   Phys. Rev. B 102, 035159 (2020)
   arXiv:2002.07637PDFDOI

   Resumen

   By reverse-engineering from exact solutions we obtain Hartree-exchange-correlation (Hxc) potentials for a double quantum dot subject to generic density-density interactions and Hund's rule coupling. We find ubiquitous step structures of the Hxc potentials that can be understood and derived from an analysis of stability diagrams. We further show that a generic Hxc potential can be decomposed into four basic potentials which allows for a straight-forward parametrization and paves the road for the construction of Hxc potentials for interacting multi-orbital systems. Finally we employ our parametrization of the Hxc potential in density functional theory calculations of multi-orbital quantum dots and find excellent agreement with exact many-body calculations.

   BibTeX

   @article{Sobrino2020exchange,
     title         = {{Exchange-correlation potentials for multi-orbital quantum dots subject to generic density-density interactions and Hund's rule coupling}},
     author        = {Nahual Sobrino and Stefan Kurth and David Jacob},
     journal       = {Phys. Rev. B},
     volume        = {102},
     pages         = {035159},
     year          = {2020},
     doi           = {10.1103/PhysRevB.102.035159},
     eprint        = {2002.07637},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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2. Analytical Shannon information entropies for all discrete multidimensional hydrogenic states
   Irene V. Toranzo, David Puertas-Centeno, Nahual Sobrino, Jesús S. Dehesa
   Int. J. Quantum Chem. 120, e26077 (2020)
   arXiv:1909.11660PDFDOI

   Resumen

   The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty measure to quantify the electronic spreading and to mathematically formalize the Heisenberg uncertainty principle, partially because it does not depend on any specific point of their multidimensional domain of definition. In this work the radial and angular parts of the Shannon entropies for all the discrete stationary states of the multidimensional hydrogenic systems are obtained from first principles; that is, they are given in terms of the states' principal and magnetic hyperquantum numbers $(n,μ_1,μ_2,\ldots,μ_{D-1})$, the system's dimensionality $D$ and the nuclear charge $Z$ in an analytical, compact form. Explicit expressions for the total Shannon entropies are given for the quasi-spherical states, which conform a relevant class of specific states of the $D$-dimensional hydrogenic system characterized by the hyperquantum numbers $μ_1=μ_2\ldots=μ_{D-1}=n-1$, including the ground state.

   BibTeX

   @article{Toranzo2020analytical,
     title         = {{Analytical Shannon information entropies for all discrete multidimensional hydrogenic states}},
     author        = {Irene V. Toranzo and David Puertas-Centeno and Nahual Sobrino and Jesús S. Dehesa},
     journal       = {Int. J. Quantum Chem.},
     volume        = {120},
     pages         = {e26077},
     year          = {2020},
     doi           = {10.1002/qua.26077},
     eprint        = {1909.11660},
     archivePrefix = {arXiv},
     primaryClass  = {quant-ph}
   }

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2019

1. Steady-state density functional theory for thermoelectric effects
   Nahual Sobrino, Roberto D'Agosta, Stefan Kurth
   Phys. Rev. B 100, 195142 (2019)
   arXiv:1909.11019PDFDOI

   Resumen

   The recently proposed density functional theory for steady-state transport (i-DFT) is extended to include temperature gradients between the leads. Within this framework, a general and exact expression is derived for the linear Seebeck coefficient which can be written as the sum of the Kohn-Sham coefficient and an exchange-correlation contribution. The formalism is applied to the single-impurity Anderson model for which approximate exchange-correlation functionals are suggested for temperatures both above and below the Kondo temperature. A certain structural property of the exchange-correlation potentials in the Coulomb blockade regime allows to recover an earlier result expressing the Seebeck coefficient in terms of quantities of equilibrium density functional theory. The numerical i-DFT results are compared to calculations with the numerical renormalization group over a wide range of temperatures finding a reasonable agreement while i-DFT comes at a much lower computational cost.

   BibTeX

   @article{Sobrino2019steady,
     title         = {{Steady-state density functional theory for thermoelectric effects}},
     author        = {Nahual Sobrino and Roberto D'Agosta and Stefan Kurth},
     journal       = {Phys. Rev. B},
     volume        = {100},
     pages         = {195142},
     year          = {2019},
     doi           = {10.1103/PhysRevB.100.195142},
     eprint        = {1909.11019},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.str-el}
   }

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2. Non-equilibrium spectral functions from multi-terminal steady-state density functional theory
   Stefan Kurth, David Jacob, Nahual Sobrino, Gianluca Stefanucci
   Phys. Rev. B 100, 085114 (2019)
   arXiv:1905.13070PDFDOI

   Resumen

   Multi-terminal transport setups allow to realize more complex measurements and functionalities (e.g., transistors) of nanoscale systems than the simple two-terminal arrangement. Here the steady-state density functional formalism (i-DFT) for the description of transport through nanoscale junctions with an arbitrary number of leads is developed. In a three-terminal setup and in the ideal STM limit where one of the electrodes (the `STM tip') is effectively decoupled from the junction, the formalism allows to extract its non-equilibrium spectral function (at arbitrary temperature) while a bias is applied between the other two electrodes. Multi-terminal i-DFT is shown to be capable of describing the splitting of the Kondo resonance in an Anderson impurity in the presence of an applied bias voltage, as predicted by numerically exact many-body approaches.

   BibTeX

   @article{Kurth2019equilibrium,
     title         = {{Non-equilibrium spectral functions from multi-terminal steady-state density functional theory}},
     author        = {Stefan Kurth and David Jacob and Nahual Sobrino and Gianluca Stefanucci},
     journal       = {Phys. Rev. B},
     volume        = {100},
     pages         = {085114},
     year          = {2019},
     doi           = {10.1103/PhysRevB.100.085114},
     eprint        = {1905.13070},
     archivePrefix = {arXiv},
     primaryClass  = {cond-mat.mes-hall}
   }

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2017

1. Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems
   N. Sobrino-Coll, D. Puertas-Centeno, I. V. Toranzo, J. S. Dehesa
   J. Stat. Mech. 2017, 083102 (2017)
   arXiv:1708.07299PDFDOI

   Resumen

   In this work we find that not only the Heisenberg-like uncertainty products and the Rényi-entropy-based uncertainty sum have the same first-order values for all the quantum states of the $D$-dimensional hydrogenic and oscillator-like systems, respectively, in the pseudoclassical ($D \to \infty$) limit but a similar phenomenon also happens for both the Fisher-information-based uncertainty product and the Shannon-entropy-based uncertainty sum, as well as for the Crámer-Rao and Fisher-Shannon complexities. Moreover, we show that the LMC (López-Ruiz-Mancini-Calvet) and LMC-Rényi complexity measures capture the hydrogenic-harmonic difference in the high dimensional limit already at first order.

   BibTeX

   @article{SobrinoColl2017complexity,
     title         = {{Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems}},
     author        = {N. Sobrino-Coll and D. Puertas-Centeno and I. V. Toranzo and J. S. Dehesa},
     journal       = {J. Stat. Mech.},
     volume        = {2017},
     pages         = {083102},
     year          = {2017},
     doi           = {10.1088/1742-5468/aa7df4},
     eprint        = {1708.07299},
     archivePrefix = {arXiv},
     primaryClass  = {quant-ph}
   }

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