scholarly journals Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Parijat Banerjee ◽  
Adwait Gaikwad ◽  
Anurag Kaushal ◽  
Gautam Mandal
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Power Law ◽  
Cold Atom ◽  
Quantum Field ◽  
Approach To Equilibrium ◽  
Zero Mass ◽  
Quantum Quench ◽  
Spatial Dimensions ◽  
Arbitrary Dimensions

Abstract In many quantum quench experiments involving cold atom systems the post-quench phase can be described by a quantum field theory of free scalars or fermions, typically in a box or in an external potential. We will study mass quench of free scalars in arbitrary spatial dimensions d with particular emphasis on the rate of relaxation to equilibrium. Local correlators expectedly equilibrate to GGE; for quench to zero mass, interestingly the rate of approach to equilibrium is exponential or power law depending on whether d is odd or even respectively. For quench to non-zero mass, the correlators relax to equilibrium by a cosine-modulated power law, for all spatial dimensions d, even or odd. We briefly discuss generalization to O(N ) models.

scholarly journals Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory.

1998 ◽  
Vol 10 (06) ◽  
pp. 775-800 ◽  
Author(s):  
D. Buchholz ◽  
R. Verch
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Short Distance ◽  
Relativistic Quantum ◽  
Free Field ◽  
Scaling Limit ◽  
Quantum Field ◽  
Algebraic Quantum ◽  
Spatial Dimensions ◽  
Local Observables

The concept of scaling algebra provides a novel framework for the general structural analysis and classification of the short distance properties of algebras of local observables in relativistic quantum field theory. In the present article this method is applied to the simple example of massive free field theory in s=1,2 and 3 spatial dimensions. Not quite unexpectedly, one obtains for s=2,3 in the scaling (short distance) limit the algebra of local observables in massless free field theory. The case s=1 offers, however, some surprises. There the algebra of observables acquires in the scaling limit a non-trivial center and describes charged physical states satisfying Gauss' law. The latter result is of relevance for the interpretation of the Schwinger model at short distances and illustrates the conceptual and computational virtues of the method.

scholarly journals Lie Group Classification of Generalized Variable Coefficient Korteweg-de Vries Equation with Dual Power-Law Nonlinearities with Linear Damping and Dispersion in Quantum Field Theory

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 83
Author(s):  
Oke Davies Adeyemo ◽  
Chaudry Masood Khalique
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Power Law ◽  
Lie Group ◽  
Variable Coefficient ◽  
Variable Coefficients ◽  
Group Classification ◽  
Quantum Field ◽  
Lie Group Classification

Many physical phenomena in fields of studies such as optical fibre, solid-state physics, quantum field theory and so on are represented using nonlinear evolution equations with variable coefficients due to the fact that the majority of nonlinear conditions involve variable coefficients. In consequence, this article presents a complete Lie group analysis of a generalized variable coefficient damped wave equation in quantum field theory with time-dependent coefficients having dual power-law nonlinearities. Lie group classification of two distinct cases of the equation was performed to obtain its kernel algebra. Thereafter, symmetry reductions and invariant solutions of the equation were obtained. We also investigate various soliton solutions and their dynamical wave behaviours. Further, each class of general solutions found is invoked to construct conserved quantities for the equation with damping term via direct technique and homotopy formula. In addition, Noether’s theorem is engaged to furnish more conserved currents of the equation under some classifications.

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