Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMicroscopic theory of non-adiabatic response in real and imaginary time
286
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a general approach to describe slowly driven quantum systems both in real and imaginary time. We highlight many similarities, qualitative and quantitative, between real and imaginary time evolution. We discuss how the metric tensor and the Berry curvature can be extracted from both real and imaginary time simulations as a response of physical observables. For quenches ending at or near the quantum critical point, we show the utility of the scaling theory for detecting the location of the quantum critical point by comparing sweeps at different velocities. We briefly discuss the universal relaxation to equilibrium of systems after a quench. We finally review recent developments of quantum Monte Carlo methods for studying imaginary-time evolution. We illustrate our findings with explicit calculations using the transverse field Ising model in one dimension.
rate research
Read More
The problem of calculating real-time correlation functions is formulated in terms of an imaginary-time partial differential equation. The latter is solved analytically for the perturbed harmonic oscillator and compared with the known exact result. The first order approximation for the short-time propagator is derived and used for numerical solution of the equation by a Monte Carlo integration. In general, the method provides a reformulation of the dynamic sign problem, and is applicable to any two-time correlation function including single-particle, density-density, current-current, spin-spin, and others. The prospects of extending the technique onto multi-dimensional problems are discussed.
In this work, we show that a universal quantum work relation for a quantum system driven arbitrarily far from equilibrium extend to $mathcal{PT}$-symmetric quantum system with unbroken $mathcal{PT}$ symmetry, which is a consequence of microscopic reversibility. The quantum Jarzynski equality, linear response theory and Onsager reciprocal relations for the $mathcal{PT}$-symmetric quantum system are recovered as special cases of the universal quantum work relation in $mathcal{PT}$-symmetric quantum system. In the regime of broken $mathcal{PT}$ symmetry, the universal quantum work relation does not hold as the norm is not preserved during the dynamics.
Fluctuation dissipation theorems connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a fluctuation dissipation theorem for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.
Reaction-diffusion systems which include processes of the form A+A->A or A+A->0 are characterised by the appearance of `imaginary multiplicative noise terms in an effective Langevin-type description. However, if `real as well as `imaginary noise is present, then competition between the two could potentially lead to novel behaviour. We thus investigate the asymptotic properties of the following two `mixed noise reaction-diffusion systems. The first is a combination of the annihilation and scattering processes 2A->0, 2A->2B, 2B->2A, and 2B->0. We demonstrate (to all orders in perturbation theory) that this system belongs to the same universality class as the single species annihilation reaction 2A->0. Our second system consists of competing annihilation and fission processes, 2A->0 and 2A->(n+2)A, a model which exhibits a transition between active and absorbing phases. However, this transition and the active phase are not accessible to perturbative methods, as the field theory describing these reactions is shown to be non-renormalisable. This corresponds to the fact that there is no stationary state in the active phase, where the particle density diverges at finite times. We discuss the implications of our analysis for a recent study of another active / absorbing transition in a system with multiplicative noise.
The emph{ab initio} path integral Monte Carlo (PIMC) approach is one of the most successful methods in quantum many-body theory. A particular strength of this method is its straightforward access to imaginary-time correlation functions (ITCF). For example, the well-known density-density ITCF $F(mathbf{q},tau)$ allows one to estimate the linear response of a given system for all wave vectors $mathbf{q}$ from a single simulation of the unperturbed system. Moreover, it constitutes the basis for the reconstruction of the dynamic structure factor $S(mathbf{q},omega)$ -- a key quantity in state-of-the-art scattering experiments. In this work, we present analogous relations between the nonlinear density response in quadratic and cubic order of the perturbation strength and generalized ITCFs measuring correlations between up to four imaginary-time arguments. As a practical demonstration of our new approach, we carry out simulations of the warm dense electron gas and find excellent agreement with previous PIMC results that had been obtained with substantially larger computational effort. In addition, we give a relation between a cubic ITCF and the triple dynamic structure factor $S(mathbf{q}_1,omega_1;mathbf{q}_2,omega_2)$, which evokes the enticing possibility to study dynamic three-body effects on an emph{ab initio} level.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
