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Heat transport through an open coupled scalar field theory hosting stability-to-instability transition (2402.04986v1)

Published 7 Feb 2024 in cond-mat.stat-mech and quant-ph

Abstract: We investigate heat transport through a one-dimensional open coupled scalar field theory, depicted as a network of harmonic oscillators connected to thermal baths at the boundaries. The non-Hermitian dynamical matrix of the network undergoes a stability-to-instability transition at the exceptional points as the coupling strength between the scalar fields increases. The open network in the unstable regime, marked by the emergence of inverted oscillator modes, does not acquire a steady state, and the heat conduction is then unbounded for general bath couplings. In this work, we engineer a unique bath coupling where a single bath is connected to two fields at each edge with the same strength. This configuration leads to a finite steady-state heat conduction in the network, even in the unstable regime. We also study general bath couplings, e.g., connecting two fields to two separate baths at each boundary, which shows an exciting signature of approaching the unstable regime for massive fields. We derive analytical expressions for high-temperature classical heat current through the network for different bath couplings at the edges and compare them. Furthermore, we determine the temperature dependence of low-temperature quantum heat current in different cases. Our study will help to probe topological phases and phase transitions in various quadratic Hermitian bosonic models whose dynamical matrices resemble non-Hermitian Hamiltonians, hosting exciting topological phases.

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References (37)
  1. N. Hatano and D. R. Nelson, Localization transitions in non-Hermitian quantum mechanics, Phys. Rev. Lett. 77, 570 (1996).
  2. C. M. Bender and S. Boettcher, Real spectra in non-Hermitian Hamiltonians having PT symmetry, Phys. Rev. Lett. 80, 5243 (1998).
  3. A. Khare and B. P. Mandal, A PT-invariant potential with complex QES eigenvalues, Phys. Lett. A 272, 53 (2000).
  4. B. Bagchi, F. Cannata, and C. Quesne, PT-symmetric sextic potentials, Phys. Lett. A 269, 79 (2000).
  5. A. Mostafazadeh, Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian, J. Math. Phys. 43, 205 (2002).
  6. C. M. Bender, M. V. Berry, and A. Mandilara, Generalized PT symmetry and real spectra, J. Phys. A: Math. Gen. 35, L467 (2002).
  7. M. Berry, Physics of non-Hermitian degeneracies, Czechoslov. J. Phys. 54, 1039 (2004).
  8. W. D. Heiss, The physics of exceptional points, J. Phys. A: Math. Theor. 45, 444016 (2012).
  9. M. S. Rudner and L. S. Levitov, Topological transition in a non-Hermitian quantum walk, Phys. Rev. Lett. 102, 065703 (2009).
  10. S.-D. Liang and G.-Y. Huang, Topological invariance and global Berry phase in non-Hermitian systems, Phys. Rev. A 87, 012118 (2013).
  11. H. Shen, B. Zhen, and L. Fu, Topological band theory for non-Hermitian Hamiltonians, Phys. Rev. Lett. 120, 146402 (2018).
  12. S. Lieu, Topological phases in the non-Hermitian Su-Schrieffer-Heeger model, Phys. Rev. B 97, 045106 (2018a).
  13. V. M. Vyas and D. Roy, Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model, Phys. Rev. B 103, 075441 (2021).
  14. R. Nehra and D. Roy, Topology of multipartite non-Hermitian one-dimensional systems, Phys. Rev. B 105, 195407 (2022).
  15. J. Colpa, Diagonalization of the quadratic boson hamiltonian, Physica A: Statistical Mechanics and its Applications 93, 327 (1978).
  16. R. Rossignoli and A. M. Kowalski, Complex modes in unstable quadratic bosonic forms, Phys. Rev. A 72, 032101 (2005).
  17. A. McDonald, T. Pereg-Barnea, and A. A. Clerk, Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain, Phys. Rev. X 8, 041031 (2018).
  18. S. Lieu, Topological symmetry classes for non-Hermitian models and connections to the bosonic bogoliubov–de gennes equation, Phys. Rev. B 98, 115135 (2018b).
  19. Y.-X. Wang and A. A. Clerk, Non-Hermitian dynamics without dissipation in quantum systems, Phys. Rev. A 99, 063834 (2019).
  20. V. P. Flynn, E. Cobanera, and L. Viola, Deconstructing effective non-Hermitian dynamics in quadratic bosonic Hamiltonians, New J. Phys. 22, 083004 (2020).
  21. V. P. Flynn, E. Cobanera, and L. Viola, Topology by dissipation: Majorana bosons in metastable quadratic markovian dynamics, Phys. Rev. Lett. 127, 245701 (2021).
  22. M. E. Peskin and D. V. Schroeder, An Introduction to quantum field theory (Addison-Wesley, Reading, USA, 1995).
  23. M. D. Schwartz, Quantum Field Theory and the Standard Model (Cambridge University Press, 2014).
  24. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  25. G. Barton, Quantum mechanics of the inverted oscillator potential, Ann. Physics 166, 322 (1986).
  26. S. Lepri, R. Livi, and A. Politi, Thermal conduction in classical low-dimensional lattices, Phys. Rep. 377, 1 (2003).
  27. A. Dhar, Heat transport in low-dimensional systems, Adv. Phys. 57, 457 (2008).
  28. A. Dhar and D. Roy, Heat transport in harmonic lattices, J. Stat. Phys. 125, 801 (2006).
  29. L.-C. Qu, J. Chen, and Y.-X. Liu, Chaos and complexity for inverted harmonic oscillators, Phys. Rev. D 105, 126015 (2022).
  30. D. Roy and A. Dhar, Heat transport in ordered harmonic lattices, J. Stat. Phys. 131, 535 (2008a).
  31. A. Dhar, Heat conduction in the disordered harmonic chain revisited, Phys. Rev. Lett. 86, 5882 (2001).
  32. D. Roy and A. Dhar, Role of pinning potentials in heat transport through disordered harmonic chains, Phys. Rev. E 78, 051112 (2008b).
  33. A. Casher and J. L. Lebowitz, Heat flow in regular and disordered harmonic chains, J. Math. Phys. 12, 1701 (1971).
  34. G. Y. Hu and R. F. O’Connell, Analytical inversion of symmetric tridiagonal matrices, J. Phys. A: Math. Gen. 29, 1511 (1996).
  35. X. Liu, S. D. Gupta, and G. S. Agarwal, Regularization of the spectral singularity in 𝒫⁢𝒯𝒫𝒯\mathcal{PT}caligraphic_P caligraphic_T-symmetric systems by all-order nonlinearities: Nonreciprocity and optical isolation, Phys. Rev. A 89, 013824 (2014).
  36. R. H. Jonsson, L. Hackl, and K. Roychowdhury, Entanglement dualities in supersymmetry, Phys. Rev. Res. 3, 023213 (2021).
  37. R. Nehra and D. Roy, Anomalous dynamical response of non-Hermitian topological phases (2023), arXiv:2310.12633 [cond-mat.mes-hall] .

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