Out-of-equilibrium dynamics of the XY spin chain from form factor expansion

We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides a natural and unified framework for out-of-equilibrium physics in this model. We show that all correlation functions in the CE can be computed using form factor expansion and expressed in terms of Fredholm determinants. In particular, we present exact out-of-equilibrium expressions in the thermodynamic limit for the previously unknown order parameter 1-point function, dynamical 2-point function and equal-time 3-point function.

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Nonstationary Superconductivity: Quantum Dissipation and Time-Dependent Ginzburg-Landau Equation

Advances in Condensed Matter Physics ◽

10.1155/2011/425328 ◽

2011 ◽

Vol 2011 ◽

pp. 1-10

Author(s):

Anatoly A. Barybin

Keyword(s):

Order Parameter ◽

Continuity Equation ◽

Chemical Potential ◽

Landau Equation ◽

Time Dependent ◽

Quantum Dissipation ◽

Ginzburg Landau ◽

Superfluid Component ◽

Ginzburg Landau Equation ◽

Conservation Property

Transport equations of the macroscopic superfluid dynamics are revised on the basis of a combination of the conventional (stationary) Ginzburg-Landau equation and Schrödinger's equation for the macroscopic wave function (often called the order parameter) by using the well-known Madelung-Feynman approach to representation of the quantum-mechanical equations in hydrodynamic form. Such an approach has given (a) three different contributions to the resulting chemical potential for the superfluid component, (b) a general hydrodynamic equation of superfluid motion, (c) the continuity equation for superfluid flow with a relaxation term involving the phenomenological parameters and , (d) a new version of the time-dependent Ginzburg-Landau equation for the modulus of the order parameter which takes into account dissipation effects and reflects the charge conservation property for the superfluid component. The conventional Ginzburg-Landau equation also follows from our continuity equation as a particular case of stationarity. All the results obtained are mutually consistent within the scope of the chosen phenomenological description and, being model-neutral, applicable to both the low- and high- superconductors.

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BERRY PHASE AND CRITICAL BEHAVIOR OF THE XY SPIN CHAIN WITH THREE-SITE INTERACTION

Modern Physics Letters B ◽

10.1142/s0217984912501412 ◽

2012 ◽

Vol 26 (22) ◽

pp. 1250141 ◽

Cited By ~ 2

Author(s):

HANLI LIAN

Keyword(s):

Spin Chain ◽

Berry Phase ◽

Finite Size ◽

Transverse Magnetic ◽

Anomalous Behavior ◽

Quantum Criticality ◽

Critical Properties ◽

Finite Size Scaling ◽

Surrounding Environment ◽

Xy Spin Chain

By calculating the Berry Phase (BP) of a central spin, the quantum criticality of the surrounding environment described by an XY spin chain with the three-site interaction in a transverse magnetic field is explored. The BP presents anomalous behavior along the critical region. The finite-size scaling behaviors suggest that the BP of the central spin can well capture the critical properties of the XY spin chain with the three-site interaction.

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Soliton dynamics and elastic collisions in a spin chain with an external time-dependent magnetic field

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2009.09.025 ◽

2010 ◽

Vol 389 (3) ◽

pp. 367-374 ◽

Cited By ~ 5

Author(s):

Hai-Qiang Zhang ◽

Bo Tian ◽

Xing Lü ◽

Xiang-Hua Meng

Keyword(s):

Magnetic Field ◽

Spin Chain ◽

Time Dependent ◽

Elastic Collisions ◽

Soliton Dynamics ◽

External Time

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WIGNER MEASURES AND MOLECULAR PROPAGATION THROUGH GENERIC ENERGY LEVEL CROSSINGS

Reviews in Mathematical Physics ◽

10.1142/s0129055x03001904 ◽

2003 ◽

Vol 15 (10) ◽

pp. 1285-1317 ◽

Cited By ~ 4

Author(s):

CLOTILDE FERMANIAN KAMMERER

Keyword(s):

Energy Transfer ◽

Normal Form ◽

Energy Level ◽

Point Of View ◽

Time Dependent ◽

Type B ◽

Unified Framework ◽

Level Crossings ◽

Normal Form Theorem ◽

Uniformly Bounded

We study the time-dependent Schrödinger equation with matrix-valued potential presenting a generic crossing of type B, I, J or K in Hagedorn's classification. We use two-scale Wigner measures for describing the Landau–Zener energy transfer which occurs at the crossing. In particular, in the case of multiplicity 2 eigenvalues, we calculate precisely the change of polarization at the crossing. Our method provides a unified framework in which codimension 2, 3 or 5 crossings can be discussed. We recover Hagedorn's result for wave packets, from Wigner measure point of view, and extend them to any data uniformly bounded in L2. The proof is based on a normal form theorem which reduces the problem to an operator-valued Landau–Zener formula.

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Josephson oscillations in split one-dimensional Bose gases

SciPost Physics ◽

10.21468/scipostphys.10.4.090 ◽

2021 ◽

Vol 10 (4) ◽

Author(s):

Yuri Daniel van Nieuwkerk ◽

Jörg Schmiedmayer ◽

Fabian Essler

Keyword(s):

Three Dimensional ◽

Time Dependent ◽

Dimensional Theory ◽

Bose Gases ◽

Microscopic Description ◽

One Dimensional ◽

Hartree Fock ◽

Equilibrium Dynamics ◽

Self Consistent ◽

Double Well Potential

We consider the non-equilibrium dynamics of a weakly interacting Bose gas tightly confined to a highly elongated double well potential. We use a self-consistent time-dependent Hartree--Fock approximation in combination with a projection of the full three-dimensional theory to several coupled one-dimensional channels. This allows us to model the time-dependent splitting and phase imprinting of a gas initially confined to a single quasi one-dimensional potential well and obtain a microscopic description of the ensuing damped Josephson oscillations.

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