Energy transfer in open quantum systems weakly coupled with two reservoirs
-
Franco Fagnola
franco.fagnola@polimi.it
-
Damiano Poletti
damiano.poletti@polimi.it
-
Emanuela Sasso
sasso@dima.unige.it
Downloads
DOI:
https://doi.org/10.4067/S0719-06462021000100121Abstract
We show that the energy transfer through an open quantum system with non-degenerate Hamiltonian weakly coupled with two reservoirs in equilibrium is approximately proportional to the difference of their temperatures unless both temperatures are small.
Keywords
L. Accardi, F. Fagnola, and R. Quezada, “On three new principles in non-equilibrium statistical mechanics and Markov semigroups of weak coupling limit type”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., vol. 19, no. 2, 1650009, 2016. DOI: 10.1142/S0219025716500090.
L. Accardi, Y. G. Lu, and I. V. Volovich, Quantum theory and its stochastic limit, Springer- Verlag, Berlin, 2002.
I. Ya. Aref‘eva, I. V. Volovich, and S. V. Kozyrev, “Stochastic Limit Method and Interference in Quantum Many Particle Systems”, Teor. Mat. Fiz., vol. 185, pp. 388–408, 2015. DOI: 10.1007/s11232-015-0296-9
G. Basile, and S. Olla, “Energy diffusion in harmonic system with conservative noise”, J. Stat. Phys., vol. 155, pp. 1126–1142, 2014. DOI: 10.1007/s10955-013-0908-4
F. Benatti, R. Floreanini, and L. Memarzadeh, “Bath assisted transport in a three-site spin chain: global vs local approach”, Phys. Rev. A, vol. 102, 042219-1–042219-14, 2020. DOI: 10.1103/PhysRevA.102.042219
G. Benenti, G. Casati, T. Prosen, and D. Rossini, “Negative differential conductivity in far-from-equilibrium quantum spin chains”, EPL, vol. 85, 37001, 2009. DOI: 10.1209/0295- 5075/85/37001
C. Bernardin, and S. Olla, “Fourier‘s Law for a Microscopic Model of Heat Conduction”, J. Stat. Phys., vol. 121, pp. 271–289, 2005. DOI: 10.1007/s10955-005-7578-9
R. Carbone, E. Sasso, and V. Umanit`a, “Structure of generic quantum Markov semigroup”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., vol. 20, no. 2, 1750012, 2017. DOI: 10.1142/S0219025717500126
J. DereziÅ„ski, and W. Roeck, “Extended Weak Coupling Limit for Pauli-Fierz Operators”, Comm. Math. Phys., vol. 279, pp. 1–30, 2008. DOI: 10.1007/s00220-008-0419-3
J. DereziÅ„ski, W. Roeck, and C. Maes, “Fluctuations of quantum currents and unravelings of master equations”, J. Stat. Phys., vol. 131, pp. 341–356, 2008. DOI: 10.1007/s10955-008- 9500-8
J. Deschamps, F. Fagnola, E. Sasso, and V. Umanit`a, “Structure of uniformly continuous quantum Markov semigroups”, Rev. Math. Phys., vol. 28, no. 1, 1650003, 2016. DOI: 10.1142/S0129055X16500033
A. Dhar, and H. Spohn, “Fourier‘s law based on microscopic dynamics”, C. R. Phys., vol. 20, pp. 393–401, 2019. DOI: 10.1016/j.crhy.2019.08.004
E. B. Davies, “Markovian Master Equations”, Comm. Math. Phys., vol. 39, pp. 91–110, 1974. projecteuclid.org/euclid.cmp/1103860160
G. S. Engel, T. R. Calhoun, E. L. Read, T. -K. Ahn, T. Mancal, Y. -C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for Wavelike Energy Transfer Through Quantum Coherence in Photosynthetic Systems”, Nature, vol. 446, pp. 782–786, 2007. DOI: 10.1038/na- ture05678
F. Fagnola, and R. Rebolledo, “Entropy Production for Quantum Markov Semigroups”, Commun. Math. Phys., vol. 335, pp. 547–570, 2015. DOI: 10.1007/s00220-015-2320-1
F. Fagnola, and R. Rebolledo, “Entropy production and detailed balance for a class of quantum Markov semigroups”, Open Syst. Inf. Dyn., vol. 22, no. 3, 1550013, 2015. DOI: 10.1142/S1230161215500134
V. Gorini, A. Kossakowski, and E.C.G. Sudarshan, “Completely positive dynamical semigroups of N-level systems”, J. Math. Phys., vol. 17, pp. 821–825, 1976. DOI: 10.1063/1.522979
J. M. Horowitz, and J. M. R. Parrondo, “Entropy production along nonequilibrium quantum jump trajectories”, New J. Phys. vol. 15, 085028, 2013. DOI: 10.1088/1367-2630/15/8/085028
V. Jakšić, C.-A. Pillet, and M. Westrich, “Entropic Fluctuations of Quantum Dynamical Semigroups”. J. Stat. Phys., vol. 154, pp. 153–187, 2014. DOI: 10.1007/s10955-013-0826-5
D. Karevski, and T. Platini, “Quantum nonequilibrium steady states induced by repeated interactions”. Phys. Rev. Lett., vol. 102, 207207-1–20207-4, 2009, DOI: 10.1103/Phys- RevLett.102.207207
E. Langmann, J. L. Lebowitz, V. Mastropietro, and P. Moosavi, “Steady States and Universal Conductance in a Quenched Luttinger Model”, Commun. Math. Phys., vol. 349, pp. 551–582, 2017. DOI: 10.1007/s00220-016-2631-x
G. Lindblad, “On the Generators of Quantum Dynamical Semigroups”, Commun. Math. Phys., vol. 48, pp. 119-130, 1976. DOI: 10.1007/BF01608499
M. Ohya, and D. Petz Quantum Entropy and its Use. Springer-Verlag, Berlin, 1993.
G. D. Scholes, G. R. Fleming, A. Olaya-Castro, and R. van Grondelle, “Lessons from Nature about Solar Light Harvesting”, Nature Chem., vol. 3, pp 763–774, 2011. DOI: doi.org/10.1038/nchem.1145
H. Spohn, and J. L. Lebowitz, “Irreversible Thermodynamics for Quantum Systems Weakly Coupled to Thermal Reservoirs”. In, Advances in Chemical Physics, S.A. Rice (Ed.) pp. 109–142, 1978. DOI: doi.org/10.1002/9780470142578.ch2
A. S. Trusheckin, “On the General Definition of the Production of Entropy in Open Markov Quantum Systems”, J. Math. Sci. (N.Y.), vol. 241, pp. 191–209, 2019. DOI: 10.1007/s10958- 019-04417-4
M. Vanicat, L. Zadnik, and T. Prosen, “Integrable trotterization: local conservation laws and boundary driving”, Phys. Rev. Lett. vol.121, 030606-1–030606-6, 2018. DOI: 10.1103/Phys- RevLett.121.030606
Similar Articles
- Laurent Amour, Benoit Grébert, Jean-Claude Guillot, A mathematical model for the Fermi weak interactions , CUBO, A Mathematical Journal: Vol. 9 No. 2 (2007): CUBO, A Mathematical Journal
- Rodrigue Sanou, Idrissa Ibrango, Blaise Koné, Aboudramane Guiro, Weak solutions to Neumann discrete nonlinear system of Kirchhoff type , CUBO, A Mathematical Journal: Vol. 21 No. 3 (2019)
- Stanislas Ouaro, Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent , CUBO, A Mathematical Journal: Vol. 14 No. 2 (2012): CUBO, A Mathematical Journal
- Chia-chi Tung, On Semisubmedian Functions and Weak Plurisubharmonicity , CUBO, A Mathematical Journal: Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal
- Mouffak Benchohra, Fatima-Zohra Mostefai, Weak Solutions of Fractional Order Pettis Integral Inclusions with Multiple Time Delay in Banach Spaces , CUBO, A Mathematical Journal: Vol. 15 No. 1 (2013): CUBO, A Mathematical Journal
- Toka Diagana, Ahmed Mohamed, Pseudo-almost automorphic solutions to some second-order differential equations , CUBO, A Mathematical Journal: Vol. 13 No. 3 (2011): CUBO, A Mathematical Journal
- Binayak Choudhury, Subhajit Kundu, Approximating a solution of an equilibrium problem by Viscosity iteration involving a nonexpansive semigroup , CUBO, A Mathematical Journal: Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal
- Aparajita Dasgupta, M.W. Wong, The semigroup and the inverse of the Laplacian on the Heisenberg group , CUBO, A Mathematical Journal: Vol. 12 No. 3 (2010): CUBO, A Mathematical Journal
- Monique Combescure, Didier Robert, Quadratic Quantum Hamiltonians revisited , CUBO, A Mathematical Journal: Vol. 8 No. 1 (2006): CUBO, A Mathematical Journal
- Peter D. Hislop, Fundamentals of scattering theory and resonances in quantum mechanics , CUBO, A Mathematical Journal: Vol. 14 No. 3 (2012): CUBO, A Mathematical Journal
You may also start an advanced similarity search for this article.