Quantum macrostatistical picture of nonequilibrium steady states

Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions. Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism, we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems. Two strategies are developed to ev…

Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states

Using the Lindblad master equation approach, we investigate the structure of steady-state solutions of open integrable quantum lattice models, driven far from equilibrium by incoherent particle reservoirs attached at the boundaries. We identify a class of boundary dissipation processes which permits to derive exact steady-state density matrices in the form of graded matrix-product operators. All the solutions factorize in terms of vacuum analogues of Baxter's Q-operators which are realized in terms of non-unitary representations of certain finite dimensional subalgebras of graded Yangians. We …

Approximating Steady States in Equilibrium and Nonequilibrium Condensates

We obtain approximations for the time-independent Gross-Pitaevskii (GP) and complex GP equation in two and three spatial dimensions by generalizing the divergence-free WKB method. The results include an explicit expression of a uniformly valid approximation for the condensate density of an ultracold Bose gas confined in a harmonic trap that extends into the classically forbidden region. This provides an accurate approximation of the condensate density that includes healing effects at leading order that are missing in the widely adopted Thomas-Fermi approximation. The results presented herein a…

密集网络上非平衡稳态的玻尔兹曼式占据

Boltzmann-Like Occupation of Nonequilibrium Steady States on Dense Networks

证明密集网络上非平衡稳态具有玻尔兹曼式占据，并揭示“低抖动”启发式的渐近精确性，将解释推广到等可及稳态。

Nonequilibrium steady states on 1-d lattice systems and Goldstone theorem

On one-dimensional two-way infinite lattice system, a property of stationary (space-) translationally invariant states with nonvanishing current expectations are investigated. We consider GNS representation with respect to such a state, on which we have a group of space-time translation unitary operators. We show, by applying Goldstone-theorem-like argument,that spectrum of the unitary operators, energy-momentum spectrum with respect to the state, has a singularity at the origin.

边界驱动电路中精确的非平衡稳态

Exact nonequilibrium steady states of boundary driven circuit with XYZ gates

本文通过空间非均匀的矩阵积Ansatz方法，精确求解了边界驱动XXZ量子电路的多体密度算符，发现了一类相对稳健的分离式手性非平衡稳态，并从实验角度具有吸引力。

Obtaining pure steady states in nonequilibrium quantum systems with strong dissipative couplings

Dissipative preparation of a pure steady state usually involves a commutative action of a coherent and a dissipative dynamics on the target state. Namely, the target pure state is an eigenstate of both the coherent and dissipative parts of the dynamics. We show that working in the Zeno regime, i.e. for infinitely large dissipative coupling, one can generate a pure state by a non commutative action, in the above sense, of the coherent and dissipative dynamics. A corresponding Zeno regime pureness criterion is derived. We illustrate the approach, looking at both its theoretical and applicative a…