Stable nonequilibrium of quantum systems

Rubén Peña, Thi Ha Kyaw, Guillermo Romero

Periodically driven quantum many-body systems exhibit novel nonequilibrium states, such as prethermalization, discrete time crystals, and many-body localization. Recently, the general mechanism of fractional resonances has been proposed that leads to slowing the many-body dynamics in systems with both U(1) and parity symmetry. Here, we show that fractional resonance is stable under local noise models. To corroborate our finding, we numerically study the dynamics of a small-scale Bose–Hubbard model that can readily be implemented in existing noisy intermediate-scale quantum (NISQ) devices. Our findings suggest a possible pathway toward a stable nonequilibrium state of matter, with potential applications of quantum memories for quantum information processing.

G. Flores-Hidalgo, Rudnei O. Ramos

Erik Schroedter, M. Bönitz, Jan‐Philip Joost

Correlated real-time dynamics in large, spatially inhomogeneous quantum systems remain difficult to access with nonequilibrium many-body methods. Two-time nonequilibrium Green functions (NEGF) retain dynamical correlations but their computational runtime grows cubically with the number of time steps $N_\mathrm{t}$. This scaling bottleneck could recently be overcome by introducing the G1--G2 scheme that is linear in $N_\mathrm{t}$, but requires propagation of a two-particle correlation function and may suffer from numerical instabilities. This has restricted simulations to small systems with $N_\mathrm{b} \sim 10^2$ basis states. Here we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted $δ$NEGF, that represents dynamical two-particle correlations through fluctuations of field-operator products, $δ\hat G$. This guarantees stable dynamics by preserving the positivity of the reduced density matrices, avoids the explicit storage of the two-particle Green function, and reduces the propagation to a finite ensemble of Hartree-Fock-like trajectories. Combined with a stochastic low-rank decomposition of the correlation functions, the method retains time-linear scaling while extending dynamical $GW$ and particle-particle and particle-hole $T$-matrix simulations to basis sizes of order $N_\mathrm{b}\sim 10^4$. We benchmark $δ$NEGF against exact and HF-GKBA results for lattice systems, finding stable correlated dynamics also at strong coupling. We further demonstrate large-scale simulations of diffusion in two-dimensional Hubbard lattices and ultrafast relaxation in graphene nanoribbon heterostructures with long-range Coulomb interactions. These results establish $δ$NEGF as a scalable route to dynamical self-energy simulations of large, spatially inhomogeneous correlated quantum systems beyond the reach of existing NEGF implementations.

Jacek Dziarmaga

Vyacheslav I. Yukalov

Elias P. Gyftopoulos, Michael R. von Spakovsky

In previous publications, it has been shown that entropy is a measure of the quantum-theoretic shape of the constituents of a system. In this paper, we present examples of quantum-theoretic shapes of some systems each consisting of one unit of a single constituent, in either a stable (thermodynamic) equilibrium state or in states that are not stable equilibrium. The systems that we consider are a structureless particle confined in either a linear box or a square box, and a harmonic oscillator. In general, we find that the shape of each constituent is “smooth”—without ripples—for each thermodynamic equilibrium state, and oscillatory or rippled for states that are either nonequilibrium or unstable equilibrium.