Study of the time evolution of correlation functions of the transverse Ising chain with ring frustration by perturbative theory

2018 ◽  
Vol 32 (10) ◽  
pp. 1850121
Author(s):  
Zhen-Yu Zheng ◽  
Peng Li
Keyword(s):  
Correlation Function ◽  
Schrödinger Equation ◽  
Time Evolution ◽  
Correlation Functions ◽  
Schrodinger Equation ◽  
Transverse Field ◽  
Time Dependent ◽  
Ising Chain ◽  
Point Correlation ◽  
Point Correlation Function

We consider the time evolution of two-point correlation function in the transverse-field Ising chain (TFIC) with ring frustration. The time-evolution procedure we investigated is equivalent to a quench process in which the system is initially prepared in a classical kink state and evolves according to the time-dependent Schrödinger equation. Within a framework of perturbative theory (PT) in the strong kink phase, the evolution of the correlation function is disclosed to demonstrate a qualitatively new behavior in contrast to the traditional case without ring frustration.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals CRITICAL BEHAVIOR IN THE ROTATING D-BRANES

1999 ◽  
Vol 14 (27) ◽  
pp. 1895-1907 ◽  
Author(s):  
RONG-GEN CAI ◽  
KWANG-SUP SOH
Keyword(s):  
Correlation Function ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Correlation Functions ◽  
Scaling Laws ◽  
Canonical Ensemble ◽  
Stable Boundary ◽  
Conformal Fields ◽  
Point Correlation ◽  
Point Correlation Function

We investigate the critical behavior near the thermodynamically stable boundary for the rotating D3-, M5- and M2-branes. The static scaling laws are found to hold. The critical exponents characterizing the scaling behaviors of susceptibilities are the same and all equal 1/2 in all cases. Using the scaling laws related to the correlation functions, we predict the critical exponents of the two-point correlation function of the corresponding conformal fields. We find that the stable boundary is shifted in the different ensembles and there does not exist the stable boundary in the canonical ensemble for the rotating M2-branes.

scholarly journals Angular distribution of scission neutrons studied with time-dependent Schrödinger equation

2018 ◽  
Vol 169 ◽  
pp. 00029
Author(s):  
Takahiro Wada ◽  
Tomomasa Asano ◽  
Nicolae Carjan
Keyword(s):  
Wave Function ◽  
Angular Distribution ◽  
Schrödinger Equation ◽  
Time Evolution ◽  
Schrodinger Equation ◽  
Initial Distribution ◽  
Time Dependent ◽  
Heavy Fragment ◽  
Fission Fragments ◽  
Asymmetric Fission

We investigate the angular distribution of scission neutrons taking account of the effects of fission fragments. The time evolution of the wave function of the scission neutron is obtained by integrating the time-dependent Schrodinger equation numerically. The effects of the fission fragments are taken into account by means of the optical potentials. The angular distribution is strongly modified by the presence of the fragments. In the case of asymmetric fission, it is found that the heavy fragment has stronger effects. Dependence on the initial distribution and on the properties of fission fragments is discussed. We also discuss on the treatment of the boundary to avoid artificial reflections

scholarly journals ON THE CONSTRUCTION OF CORRELATION FUNCTIONS FOR THE INTEGRABLE SUPERSYMMETRIC FERMION MODELS

2006 ◽  
Vol 20 (05) ◽  
pp. 505-549 ◽  
Author(s):  
SHAO-YOU ZHAO ◽  
WEN-LI YANG ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Correlation Function ◽  
Physical Properties ◽  
Correlation Functions ◽  
Recent Progress ◽  
Integrable Models ◽  
Thermodynamical Limit ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Creation ◽  
Scalar Products

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the Uq(gl(2|1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

scholarly journals Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain

2016 ◽  
Vol 1 (1) ◽  
Author(s):  
Tatjana Puskarov ◽  
Dirk Schuricht
Keyword(s):  
Time Evolution ◽  
Finite Time ◽  
Transverse Field ◽  
Transverse Magnetic ◽  
Ising Chain ◽  
Continuous Change ◽  
Time Quantum ◽  
Quantum Quenches ◽  
Point Correlation ◽  
Loschmidt Echo

We study the time evolution in the transverse-field Ising chain subject to quantum quenches of finite duration, ie, a continuous change in the transverse magnetic field over a finite time. Specifically, we consider the dynamics of the total energy, one- and two-point correlation functions and Loschmidt echo during and after the quench as well as their stationary behaviour at late times. We investigate how different quench protocols affect the dynamics and identify universal properties of the relaxation.

scholarly journals CORRELATION FUNCTIONS OF A CONFORMAL FIELD THEORY IN THREE DIMENSIONS

1996 ◽  
Vol 11 (13) ◽  
pp. 1047-1059 ◽  
Author(s):  
S. GURUSWAMY ◽  
P. VITALE
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Correlation Functions ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Radius Of Curvature ◽  
Nonlinear Sigma Model ◽  
Long Distance ◽  
Point Correlation ◽  
Point Correlation Function

We derive explicit forms of the two-point correlation functions of the O(N) nonlinear sigma model at the critical point, in the large-N limit, on various three-dimensional manifolds of constant curvature. The two-point correlation function, G(x, y), is the only n-point correlation function which survives in this limit. We analyze the short distance and long distance behaviors of G(x, y). It is shown that G(x, y) decays exponentially with the Riemannian distance on the spaces R2×S1, S1×S1×R, S2×R, H2×R. The decay on R3 is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behavior of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight [Formula: see text]; we illustrate this using the example of the manifold S2×R whose metric is conformally equivalent to that of R3–{0} up to a reparametrization.

DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS

1990 ◽  
Vol 04 (05) ◽  
pp. 1003-1037 ◽  
Author(s):  
A.R. Its ◽  
A.G. Izergin ◽  
V.E. Korepin ◽  
N.A. Slavnov
Keyword(s):  
Correlation Function ◽  
Integral Operator ◽  
Schrödinger Equation ◽  
Differential Equations ◽  
Nonlinear Schrödinger Equation ◽  
Correlation Functions ◽  
Quantum Correlation ◽  
Schrodinger Equation ◽  
Bose Gas ◽  
Nonlinear Schrodinger Equation

The quantum nonlinear Schrödinger equation (one dimensional Bose gas) is considered. Classification of representations of Yangians with highest weight vector permits us to represent correlation function as a determinant of a Fredholm integral operator. This integral operator can be treated as the Gelfand-Levitan operator for some new differential equation. These differential equations are written down in the paper. They generalize the fifth Painlève transcendent, which describe equal time, zero temperature correlation function of an impenetrable Bose gas. These differential equations drive the quantum correlation functions of the Bose gas. The Riemann problem, associated with these differential equations permits us to calculate asymp-totics of quantum correlation functions. Quantum correlation function (Fredholm determinant) plays the role of τ functions of these new differential equations. For the impenetrable Bose gas space and time dependent correlation function is equal to τ function of the nonlinear Schrödinger equation itself, For a penetrable Bose gas (finite coupling constant c) the correlator is τ-function of an integro-differentiation equation.

Sign in / Sign up

Export Citation Format

Share Document