Control of local relaxation behavior in closed bipartite quantum systems

Abstract

We investigate the decoherence of a spin- 1/2 subsystem weakly coupled to an environment of many spins- 1/2 with and without mutual coupling. The total system is closed, its state is pure, and evolves under Schrödinger dynamics. Nevertheless, the considered spin typically reaches a quasistationary equilibrium state. Here we show that this state depends strongly on the coupling to the environment on the one hand and on the coupling within the environmental spins on the other. In particular we focus on spin star and spin ring-star geometries to investigate the effect of intra-environmental coupling on the central spin. By changing the spectrum of the environment, its effect as a bath on the central spin is also changed and may even be adjustable to some degree. We find that the relaxation behavior is related to the distribution of the energy eigenstates of the total system. For each of these relaxation modes, there is a dual mode for which the resulting subsystem approaches an inverted state occupation probability (negative temperature).

Nonthermal equilibrium states of closed bipartite systems

“…Here we extend our analysis form our previous paper [13] regarding the controllability of relaxation behavior within these spin systems II. CANONICAL AND NON CANONICAL RELAXATION Figure 1 shows a two-level system (TLS) in resonant (δ S = δ C = δ) contact with an environment consisting of two "energy bands" k, k ′ of degeneracies g k , g k ′ , respectively (for simplicity we use g = g k , g ′ = g k ′ in the following, typically g ′ > g).…”

“…The λ ε -distributions of several spin-environments have been discussed in [13], so we will only discuss them briefly here.…”

“…for N environmental spins. It has been shown in [13] that if the coefficients γ (7), however with small fluctuations on the diagonal, and the interaction part of the Hamiltonian matrix is only sparsely populated. Nevertheless, the λ εdistribution shows some similarity to the one described in section IV B 2 for small level splitting.…”

Topological approach to microcanonical thermodynamics and phase transition of interacting classical spins

“…We stress that negative spin temperature states, which are "formally" allowed only for systems with an energy upper bound and spins loosely coupled to the other degrees of freedom (ideally uncoupled in our spin-only systems), were first considered in the context of experiments in nuclear spin systems [35], and subjected to an analysis of relevant aspects of their thermodynamics and statistical mechanics properties [36,37]. A variety of models predicting states with negative temperatures has attracted continuous interest: anti-shielding effect and superluminal light propagation under reversed electric fields [38], cosmological model describing dark energy and supermassive black holes [39], unconfined quark-gluon plasma [40], decoherence [41], PTs, metastability, entanglement in bipartite quantum systems [42], and optical lattices under parabolical potentials [43,30]. However, it has been shown [44] that states at negative absolute temperature (T N ) are metastable and heat can flow irreversibly to a reservoir at an absolute positive temperature (T P ).…”

Energy and entropy: Path from game theory to statistical mechanics

“…For a negative-temperature state all pairs (i, j) hold (13). Negative temperatures are known for various systems whose energies are bounded from above (e.g., spin systems) [31][32][33][34][35].…”