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Density of Bloch waves just after a quench

Jacek Dziarmaga

Published May 18, 1998• 0 citations
OpenAlex

Abstract

Production of Bloch waves during a rapid quench is studied by analytical and numerical methods. The density of Bloch waves decays exponentially with the quench time. It also strongly depends on temperature. Very few textures are produced for temperatures lower than a characteristic temperature proportional to the square of the magnetic field.

Related papers

Density of Bloch Waves after a Quench

Jacek Dziarmaga

Production of Bloch waves during a rapid quench is studied by analytical and numerical methods. The density of Bloch waves decays exponentially with the quench time. It also strongly depends on temperature. Very few textures are produced for temperatures lower than a characteristic temperature proportional to the square of the magnetic field.

arXiv:cond-mat/9805215•Physical Review Letters•Dec 21, 1998•15 citations

Density of kinks after a sudden quench in the quantum Ising spin chain

Sei Suzuki, Davide Rossini, Giuseppe E. Santoro

We investigate the time evolution of the density of kinks in the spin-1/2 quantum Ising spin chain after a sudden quench in the transverse field strength, and find that it relaxes to a value which depends on the initial and the final values of the transverse field, with an oscillating power-law decay. We provide analytical estimates of the long-time behavior and of the asymptotic value reached after complete relaxation, and discuss the role of quantum criticality in the quench dynamics. We show that, for a dynamics at the critical point, the residual density of kinks after the quench can be described by equilibrium statistical mechanics at a finite temperature dictated by the energy of the state after the quench. On the other hand, outside of criticality it does not exhibit thermalization.

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Pattern formation in charge density wave states after a quantum quench

Lingyu Yang, Yang Yang, Gia-Wei Chern

We study postquench dynamics of charge density wave (CDW) order in the square-lattice $t\text{\ensuremath{-}}V$ model. The ground state of this system at half-filling is characterized by a checkerboard modulation of particle density. A generalized self-consistent mean-field method, based on the time-dependent variational principle, is employed to describe the dynamical evolution of the CDW states. Assuming a homogeneous CDW order throughout the quench process, the time-dependent mean-field approach is reduced to the Anderson pseudospin method. Quench simulations based on the Bloch equation for pseudospins produce three canonical behaviors of order-parameter dynamics: phase-locked persistent oscillation, Landau-damped oscillation, and dynamical vanishing of the CDW order. We further develop an efficient real-space von Neumann equation method to incorporate dynamical inhomogeneity into simulations of quantum quenches. Our large-scale simulations uncover complex pattern formations in the postquench CDW states, especially in the strong quench regime. The emergent spatial textures are characterized by super density modulations on top of the short-period checkerboard CDW order. Our demonstration of pattern formation in quenched CDW states, described by a simple broken ${Z}_{2}$ symmetry, underscores the importance of dynamical inhomogeneity in quantum quenches of many-body systems with more complex orders.

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Method of solving the homogeneous Bloch equation

M. Kobayashi

A method of solving the Bloch equation with infinite relaxation times is given. Applying this method we have found unknown analytic solutions as well as the well-known solutions.

Journal of Mathematical Physics•Sep 26, 2002•6 citations
Production of Bloch waves during a rapid quench is studied by analytical and numerical methods. The density of Bloch waves decays exponentially with the quench time. It also strongly depends on temperature. Very few textures are produced for temperatures lower than a characteristic temperature proportional to the square of the magnetic field.
We investigate the time evolution of the density of kinks in the spin-1/2 quantum Ising spin chain after a sudden quench in the transverse field strength, and find that it relaxes to a value which depends on the initial and the final values of the transverse field, with an oscillating power-law decay. We provide analytical estimates of the long-time behavior and of the asymptotic value reached after complete relaxation, and discuss the role of quantum criticality in the quench dynamics. We show that, for a dynamics at the critical point, the residual density of kinks after the quench can be described by equilibrium statistical mechanics at a finite temperature dictated by the energy of the state after the quench. On the other hand, outside of criticality it does not exhibit thermalization.
We take a one-dimensional tight-binding chain with periodic boundary condition and put a particle in an arbitrary Bloch state, then quench it by suddenly changing the potential of an arbitrary site. In the ensuing time evolution, the probability density of the wave function at an arbitrary site jumps indefinitely between plateaus . This phenomenon adds to a former one in which the survival probability of the particle in the initial Bloch state shows cusps periodically, which was found in the same scenario ( Zhang J. M. and Yang H.-T. , EPL , 114 (2016) 60001). The plateaus support the scattering wave picture of the quench dynamics of the Bloch state. Underlying the cusps and jumps is the exactly solvable, nonanalytic dynamics of a Luttinger-like model, based on which, the locations of the jumps and the heights of the plateaus are accurately predicted.
We study postquench dynamics of charge density wave (CDW) order in the square-lattice $t\text{\ensuremath{-}}V$ model. The ground state of this system at half-filling is characterized by a checkerboard modulation of particle density. A generalized self-consistent mean-field method, based on the time-dependent variational principle, is employed to describe the dynamical evolution of the CDW states. Assuming a homogeneous CDW order throughout the quench process, the time-dependent mean-field approach is reduced to the Anderson pseudospin method. Quench simulations based on the Bloch equation for pseudospins produce three canonical behaviors of order-parameter dynamics: phase-locked persistent oscillation, Landau-damped oscillation, and dynamical vanishing of the CDW order. We further develop an efficient real-space von Neumann equation method to incorporate dynamical inhomogeneity into simulations of quantum quenches. Our large-scale simulations uncover complex pattern formations in the postquench CDW states, especially in the strong quench regime. The emergent spatial textures are characterized by super density modulations on top of the short-period checkerboard CDW order. Our demonstration of pattern formation in quenched CDW states, described by a simple broken Z2{Z}_{2}Z2​ symmetry, underscores the importance of dynamical inhomogeneity in quantum quenches of many-body systems with more complex orders.