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. 2016 Mar 22:6:23408.
doi: 10.1038/srep23408.

Non-hermitian quantum thermodynamics

Bartłomiej Gardas  1   2 , Sebastian Deffner  1   3 , Avadh Saxena  1   3
Affiliations

Non-hermitian quantum thermodynamics

Bartłomiej Gardas et al. Sci Rep. .

Abstract

Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose two setups to test our predictions, namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.

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Figures

Figure 1
Figure 1
Left panel: Average exponentiated work ⟨e−βW⟩ (blue curve) as a function of the number of terms Nmax included in the summation (11) for the protocol (23). The function quickly converges to e−βΔF (red curve) showing that the Jarzynski equality (12) holds. Right panel: ⟨Wirr⟩ = ⟨W⟩ − ΔF as a function of τ which relates to the speed at which the energy is supplied to the system. The irreversible work ⟨Wirr⟩ → 0 as τ approaches the quasistatic regime. The inset (red curve) shows the irreversible work calculated for a linear protocol, ω(t) = ωi + (ωf − ωi)t/τ. We see that it takes longer for the system to reach its quasistatic regime. Parameters used in the numerical simulations are: wi = 0.2, wf = 0.6, Nτ = 1.5 (left panel) and Nτ = 3. (right panel); the remaining parameters were set to 1.
Figure 2
Figure 2
Left panel: Relaxation time formula image, as a function of the final value λf for the linear quench λt = λi + (λf − λi)t/τ. Parameters are λi = 0, β = ħ = τ = 1. Inset: numerical confirmation of the Jarzynski equality (12). Right panel: In the broken regime quantum work can no longer be determined by the two-time energy measurement as ⟨ψ, gψ⟩ can be both positive and negative. To construct the plot we set g = σx. States ψ(n) have been chosen randomly; and n is an integer that has been assigned to them.
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