Geometric magnetism in open quantum systems

Campisi, Michele; Денисов, С. В.; Hänggi, Peter

doi:10.1103/physreva.86.032114

Cited by 38 publications

(47 citation statements)

References 58 publications

(114 reference statements)

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“…in Sec.III A, these properties permit to use the Riemann-Lebesgue lemma to evaluate the non-equilibrium fluctuations Υ αβ ij (t, t , t 0 ) and Ξ αβ ij (t, t , t 0 ) involved in expression (52), which are respectively obtained from the second and third line of (47) via the inverse Fourier transform. Specifically, these non-stochastic fluctuations takes the following form in the time domain, Υ αβ ij (t, t , t 0 ) = 4 π 2 dωdω Re G αβ ij (ω, ω , t 0 ) cos(ωt − ω t ) + Im G αβ ij (ω, ω , t 0 ) sin(ωt − ω t ) ,…”

Section: Appendix C: Retarded Self-energy and Spectral Densitymentioning

confidence: 99%

“…Starting from first principles, we derive a low-lying Hamiltonian that provides a reliable and (numerically) solvable dissipative microscopic description within the Langevinequation framework [5,19,22]. Interestingly, the Chern-Simons effects give rise to a Lorentz-like fluctuating force which represents an alternative to the geometric magnetism [52] in the context of recently extended environments [53,54]. Unlike previous treatments, we show that the components of such Chern-Simons (electric) force are non-commutative owing to the "topological" nature of the underlying theory, and cause an (ordinary) Hall re-sponse of the system particles that recalls the dissipative Hofstadter model [55,56].…”

Section: Introductionmentioning

confidence: 99%

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Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory

Valido¹

2019

Phys. Rev. D

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Conventional Brownian motion in harmonic systems has provided a deep understanding of a great diversity of dissipative phenomena. We address a rather fundamental microscopic description for the (linear) dissipative dynamics of two-dimensional harmonic oscillators that contains the conventional Brownian motion as a particular instance. This description is derived from first principles in the framework of the so-called Maxwell-Chern-Simons electrodynamics, or also known, Abelian topological massive gauge theory. Disregarding backreaction effects and endowing the system Hamiltonian with a suitable renormalized potential interaction, the conceived description is equivalent to a minimal-coupling theory with a gauge field giving rise to a fluctuating force that mimics the Lorentz force induced by a particle-attached magnetic flux. We show that the underlying symmetry structure of the theory (i.e. time-reverse asymmetry and parity violation) yields an interacting vortex-like Brownian dynamics for the system particles. An explicit comparison to the conventional Brownian motion in the quantum Markovian limit reveals that the proposed description represents a second-order correction to the well-known damped harmonic oscillator, which manifests that there may be dissipative phenomena intrinsic to the dimensionality of the interesting system.

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Section: Appendix C: Retarded Self-energy and Spectral Densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory

Valido¹

2019

Phys. Rev. D

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“…More recently, it has been used to investigate Jarzynski's identity [105] and Crooks' fluctuation relation [38,39] for a charged Brownian particle in a time-dependent potential or magnetic field [106,107]. The issue of geometric magnetism has also been studied with such a model [108]. Here, we are interested by the multivariate fluctuation relation in nonequilibrium steady states.…”

Section: Equation Of Motion and Fokker-planck Equationmentioning

confidence: 99%

Multivariate fluctuation relations for currents

Gaspard

2013

New J. Phys.

112

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This paper is devoted to multivariate fluctuation relations for all the currents flowing across an open system in contact with several reservoirs at different temperatures and chemical potentials, or driven by time-independent external mechanical forces. After some transient behavior, the open system is supposed to reach a nonequilibrium steady state that is controlled by the thermodynamic and mechanical forces, called the affinities. The time-reversal symmetry of the underlying Hamiltonian dynamics implies symmetry relations among the statistical properties of the fluctuating currents, depending on the values of the affinities. These multivariate fluctuation relations are not only compatible with the second law of thermodynamics, but they also imply remarkable relations between the linear or nonlinear response coefficients and the cumulants of the fluctuating currents. These relations include the Onsager and Casimir reciprocity relations, as well as their generalizations beyond linear response. Methods to deduce multivariate fluctuation relations are presented for classical, stochastic and quantum systems. In this way, multivariate fluctuation relations are obtained for energy or particle transport in the effusion of an ideal gas, heat transport in Hamiltonian systems coupled by Langevin stochastic forces to heat reservoirs, driven Brownian motion of an electrically charged particle subjected to an external magnetic field, and quantum electron transport in multi-terminal mesoscopic circuits where the link to the scattering approach is established.

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“…Nevertheless, linear response results have been more promising as only very few examples can be treated analytically in the microscopic description. In addition, descriptions by methods of linear response theory led to the discovery of new effects, as for instance geometric magnetism 32,33 . In the following we will derive an analytical and tractable expression for the irreversible work for slow, but not necessarily weak driving.…”

Section: Introductionmentioning

confidence: 99%

Optimal driving of isothermal processes close to equilibrium

Bonança

Deffner

2014

The Journal of Chemical Physics

118

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We investigate how to minimize the work dissipated during nonequilibrium processes. To this end, we employ methods from linear response theory to describe slowly varying processes, i.e., processes operating within the linear regime around quasistatic driving. As a main result we find that the irreversible work can be written as a functional that depends only on the correlation time and the fluctuations of the generalized force conjugated to the driving parameter. To deepen the physical insight of our approach we discuss various self-consistent expressions for the response function, and derive the correlation time in closed form. Finally, our findings are illustrated with several analytically solvable examples.

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Geometric magnetism in open quantum systems

Cited by 38 publications

References 58 publications

Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory

Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory

Multivariate fluctuation relations for currents

Optimal driving of isothermal processes close to equilibrium

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