Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEffective potential for dissipative quantum systems
113
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider quantum nonlinear systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas are derived in order to evaluate thermal averages of observables: the cases of linear and nonlinear dissipation are considered, and the framework is extended to the case of many degrees of freedom.
rate research
Read More
We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of cluster algorithms and the treatment of long-range interactions. Dissipative quantum spins and resistively shunted Josephson junctions will be considered.
The approach to the calculation of quantum dynamical correlation functions is presented in the framework of the Mori theory. An unified treatment of classic and quantum dynamics is given in terms of Weyl representation of operators and holomorphic variables. The range of validity of an approximate molucular dynamics is discussed
We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when the parameters of the Hamiltonian driving the unitary dynamics are close to their critical values. As paradigmatic models, we consider fermionic wires subject to dissipative interactions at the boundaries, associated with pumping or loss of particles. They are induced by couplings with a Markovian baths, so that the evolution of the system density matrix can be described by a Lindblad master equation. We study the quantum evolution arising from variations of the Hamiltonian and dissipation parameters, starting at t=0 from the ground state of the critical Hamiltonian. Two different dynamic regimes emerge: (i) an early-time regime for times t ~ L, where the competition between coherent and incoherent drivings develops a dynamic finite-size scaling, obtained by extending the scaling framework describing the coherent critical dynamics of the closed system, to allow for the boundary dissipation; (ii) a large-time regime for t ~ L^3 whose dynamic scaling describes the late quantum evolution leading to the t->infty stationary states.
We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permits to get manageable PQSCHA expressions for quantum thermal averages with a classical Boltzmann factor involving an effective potential and an inner Gaussian average that describes the fluctuations originating from the interplay of quanticity and dissipation. The application of the PQSCHA to a quantum phi4-chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth.
We present an analog of the phenomenon of orthogonality catastrophe in quantum many body systems subject to a local dissipative impurity. We show that the fidelity $F(t)$, giving a measure for distance of the time-evolved state from the initial one, displays a universal scaling form $F(t)propto t^theta e^{-gamma t}$, when the system supports long range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential fall-off at rate $gamma$ signals the onset of environmental decoherence, which is critically slowed down by the additional algebraic contribution to the fidelity. This picture is derived within a second order cumulant expansion suited for Liouvillian dynamics, and substantiated for the one-dimensional transverse field quantum Ising model subject to a local dephasing jump operator, as well as for XY and XX quantum spin chains, and for the two dimensional Bose gas deep in the superfluid phase with local particle heating. Our results hint that local sources of dissipation can be used to inspect real-time correlations and to induce a delay of decoherence in open quantum many body systems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
