scholarly journals Quantum quench in the Luttinger model with finite temperature initial state

2013 ◽  
Vol 88 (15) ◽  
Author(s):  
Ádám Bácsi ◽  
Balázs Dóra
Keyword(s):  
Finite Temperature ◽  
Initial State ◽  
Luttinger Model ◽  
Quantum Quench

scholarly journals Analysis of the buildup of spatiotemporal correlations and their bounds outside of the light cone

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Nils O. Abeling ◽  
Lorenzo Cevolani ◽  
Stefan Kehrein
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Light Cone ◽  
Relativistic Quantum ◽  
Initial State ◽  
Quantum Theories ◽  
Luttinger Model ◽  
Power Law Decay ◽  
Exactly Solvable ◽  
Exponentially Small

In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the correlation function of two local disjoint observables at different times if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interacting to the interacting model.

What is Initial State of Scattering at Finite Temperature?

1999 ◽  
Vol 16 (5) ◽  
pp. 336-338
Author(s):  
De-fu Hou ◽  
Jian Zuo ◽  
Jia-rong Li
Keyword(s):  
Finite Temperature ◽  
Initial State

SQUEEZED STATES AND UNCERTAINTY RELATION AT FINITE TEMPERATURE

1993 ◽  
Vol 08 (37) ◽  
pp. 3575-3584 ◽  
Author(s):  
B.L. HU ◽  
YUHONG ZHANG
Keyword(s):  
Finite Temperature ◽  
Uncertainty Relation ◽  
Quantum Statistical Mechanics ◽  
Thermal Fluctuations ◽  
Squeezed States ◽  
Relative Importance ◽  
Initial State ◽  
Decoherence Time ◽  
Brownian Model ◽  
Quantum Open System

We use the quantum Brownian model to derive the uncertainty relation for a quantum open system in an arbitrarily-squeezed initial state interacting with an environment at finite temperature. We examine the relative importance of the quantum and thermal fluctuations in the evolution of the system towards equilibrium with the aim of clarifying the meaning of quantum, classical and thermal. We show that upon contact with the bath the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is the same as the decoherence time calculated before in the context of quantum to classical transitions. We also use these results to deduce the conditions when the two basic postulates of quantum statistical mechanics become valid.

scholarly journals Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench

2018 ◽  
Vol 4 (3) ◽  
Author(s):  
Axel Cortes Cubero
Keyword(s):  
Effective Charge ◽  
Central Charge ◽  
Large Mass ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Temperature Dependent ◽  
Initial State ◽  
Conformal Field ◽  
Quantum Quench ◽  
Short Times

At thermal equilibrium, the concept of effective central charge for massive deformations of two-dimensional conformal field theories (CFT) is well understood, and can be defined by comparing the partition function of the massive model to that of a CFT. This temperature-dependent effective charge interpolates monotonically between the central charge values corresponding to the IR and UV fixed points at low and high temperatures, respectively. We propose a non-equilibrium, time-dependent generalization of the effective central charge for integrable models after a quantum quench, c_{\rm eff}(t), obtained by comparing the return amplitude to that of a CFT quench. We study this proposal for a large mass quench of a free boson, where the effective charge is seen to interpolate between c_{\rm eff}=0 at t=0t=0, and c_{\rm eff}\sim 1 at t\to\inftyt→∞, as is expected. We use our effective charge to define an “Ising to Tricritical Ising" quench protocol, where the charge evolves from c_{\rm eff}=1/2 at t=0t=0, to c_{\rm eff}=7/10 at t\to\inftyt→∞, the corresponding values of the first two unitary minimal CFT models. We then argue that the inverse “Tricritical Ising to Ising" quench is impossible with our methods. These conclusions can be generalized for quenches between any two adjacent unitary minimal CFT models. We finally study a large mass quench into the “staircase model" (sinh-Gordon with a particular complex coupling). At short times after the quench, the effective central charge increases in a discrete “staircase" structure, where the values of the charge at the steps can be computed in terms of the central charges of unitary minimal CFT models. When the initial state is a pure state, one always finds that c_{\rm eff}(t\to\infty)\geq c_{\rm eff}(t=0), though c_{\rm eff}(t), generally oscillates at finite times. We explore how this constraint may be related to RG flow irreversibility.

scholarly journals On computing non-equilibrium dynamics following a quench

2021 ◽  
Vol 11 (6) ◽  
Author(s):  
Neil Robinson ◽  
Albertus de Klerk ◽  
Jean-Sébastien Caux
Keyword(s):  
Numerical Approach ◽  
Solvable Models ◽  
Lattice Systems ◽  
Initial State ◽  
Numerical Renormalization Group ◽  
Equilibrium Dynamics ◽  
Quantum Quench ◽  
Truncation Scheme ◽  
Exactly Solvable ◽  
Non Equilibrium

Computing the non-equilibrium dynamics that follows a quantum quench is difficult, even in exactly solvable models. Results are often predicated on the ability to compute overlaps between the initial state and eigenstates of the Hamiltonian that governs time evolution. Except for a handful of known cases, it is generically not possible to find these overlaps analytically. Here we develop a numerical approach to preferentially generate the states with high overlaps for a quantum quench starting from the ground state or an excited state of an initial Hamiltonian. We use these preferentially generated states, in combination with a "high overlap states truncation scheme" and a modification of the numerical renormalization group, to compute non-equilibrium dynamics following a quench in the Lieb-Liniger model. The method is non-perturbative, works for reasonable numbers of particles, and applies to both continuum and lattice systems. It can also be easily extended to more complicated scenarios, including those with integrability breaking.

scholarly journals Quantum quench from a thermal initial state

2009 ◽  
Vol 87 (2) ◽  
pp. 20002 ◽  
Author(s):  
S. Sotiriadis ◽  
P. Calabrese ◽  
J. Cardy
Keyword(s):  
Initial State ◽  
Quantum Quench
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