Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect
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Springer
Received: March 6, Revised: July 10, Accepted: August 3, Published: September 3,
2020 2020 2020 2020
Parijat Banerjee,b,1 Adwait Gaikwad,a Anurag Kaushala and Gautam Mandala a
Tata Institute of Fundamental Research, Mumbai 400005, India b Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, U.S.A.
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: In many quantum quench experiments involving cold atom systems the postquench 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. Keywords: Field Theories in Higher Dimensions, Field Theories in Lower Dimensions, Integrable Field Theories ArXiv ePrint: 1910.02404
1
Work started during a research project in TIFR.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)027
JHEP09(2020)027
Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect
Contents 1 Introduction and summary
1 4 5 7 9 10 11
3 Time-dependence of two-point functions 3.1 General remarks 3.2 Critical quench correlators 3.2.1 Time-dependent part of the hφφi correlator 3.2.2 Large time behaviour for odd d 3.2.3 Large time behaviour for even d 3.2.4 ∂i φ∂i φ and ∂t φ∂t φ correlator 3.3 Massive quench correlators 3.3.1 φφ correlator 3.3.2 ∂t φ∂t φ and ∂i φ∂i φ correlators 3.4 Some comments on 2-point functions in critical vs. massive quench
11 12 14 14 14 16 19 19 20 22 23
4 The generalized Gibbs ensemble (GGE) 4.1 GGE 4.2 Equilibration to GGE
24 24 25
5 Geometrical interpretation of the correlators in the CC state 5.1 Comments on approach to thermalization and the odd-even effect 5.2 The thermal auto-correlator
26 27 30
6 Kaluza-Klein interpretation of thermal correlators
31
7 Discussion
32
A Dirichlet boundary state and relation to post-quench state
34
B Recursion relation
35
C Details of critical quench calculations C.1 2+1 dimensions C.1.1 CC state C.1.2 Ground state C.2 3+1 dimensions
36 36 36 36 37
–i–
JHEP09(2020)027
2 Quantum quench in free scalar theories: review 2.1 Quantum quench from the ground state 2.1.1 Two-point functions 2.2 More general quantum quench: from squeezed states 2.2.1 The squeezed state 2-point function 2.3 gCC correlators encompass all cases
C.2.1 CC correlator C.2.2 gCC4 correlator C.2.3 Ground state correlator C.2.4 The thermal correlator C.3 4+1 dimensions C.
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