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.
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M. Rigol, V. Dunjko, V. Yurovsky and M. Olshanii, Relaxation in a completely integrable many-body quantum system: An Ab Initio study of the dynamics of the highly excited states of 1d lattice hard-core bosons, Phys. Rev. Lett. 98 (2007) 050405 [cond-mat/0604476].
M. Rigol, V. Dunjko and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature 452 (2008) 854 [arXiv:0708.1324].
P. Calabrese and J. Cardy, Quantum quenches in extended systems, J. Stat. Mech. 2007 (2007) P06008.
T. Barthel and U. Schollwöck, Dephasing and the Steady State in Quantum Many-Particle Systems, Phys. Rev. Lett. 100 (2008) 100601 [arXiv:0711.4896].
M. Cramer, C.M. Dawson, J. Eisert and T.J. Osborne, Exact Relaxation in a Class of Nonequilibrium Quantum Lattice Systems, Phys. Rev. Lett. 100 (2008) 030602 [cond-mat/0703314] [INSPIRE].
D. Fioretto and G. Mussardo, Quantum Quenches in Integrable Field Theories, New J. Phys. 12 (2010) 055015 [arXiv:0911.3345] [INSPIRE].
A. Iucci and M.A. Cazalilla, Quantum quench dynamics of the Luttinger model, Phys. Rev. A 80 (2009) 063619 [arXiv:1003.5170].
P. Calabrese, F.H.L. Essler and M. Fagotti, Quantum quench in the transverse field Ising chain: I. Time evolution of order parameter correlators, J. Stat. Mech. 2012 (2012) P07016 [arXiv:1204.3911].
P. Calabrese, F.H.L. Essler and M. Fagotti, Quantum Quench in the Transverse Field Ising Chain, Phys. Rev. Lett. 106 (2011) 227203 [arXiv:1104.0154] [INSPIRE].
P. Calabrese, F.H.L. Essler and M. Fagotti, Quantum quenches in the transverse field Ising chain: II. Stationary state properties, J. Stat. Mech. 2012 (2012) P07022 [arXiv:1205.2211].
B. Bertini, D. Schuricht and F.H.L. Essler, Quantum quench in the sine-Gordon model, J. Stat. Mech. 1410 (2014) P10035 [arXiv:1405.4813] [INSPIRE].
C. Gogolin and J. Eisert, Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems, Rept. Prog. Phys. 79 (2016) 056001 [arXiv:1503.07538] [INSPIRE].
F.H.L. Essler, G. Mussardo and M. Panfil, Generalized Gibbs Ensembles for Quantum Field Theories, Phys. Rev. A 91 (2015) 051602 [arXiv:1411.5352] [INSPIRE].
F.H.L. Essler and M. Fagotti, Quench dynamics and relaxation in isolated integrable quantum spin chains, J. Stat. Mech. 2016 (2016) 064002.
L. Vidmar and M. Rigol, Generalized gibbs ensemble in integrable lattice models, J. Stat. Mech. 2016 (2016) 064007.
E. Ilievski, M. Medenjak, T. Prosen and L. Zadnik, Quasilocal charges in integrable lattice systems, J. Stat. Mech. 2016 (2016) 064008.
J.-S. Caux, The quench action, J. Stat. Mech. 2016 (2016) 064006.
S.U.E. Fermi, J.R. Pasta and M. Tsingou, Studies of nonlinear problems, I, Los Alamos Report, LA-1940 (1955).
T. Kinoshita, T. Wenger and D.S. Weiss, A quantum newton’s cradle, Nature 440 (2006) 900.
J. Cardy, Thermalization and Revivals after a Quantum Quench in Conformal Field Theory, Phys. Rev. Lett. 112 (2014) 220401 [arXiv:1403.3040] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
P. Calabrese and J.L. Cardy, Time-dependence of correlation functions following a quantum quench, Phys. Rev. Lett. 96 (2006) 136801 [cond-mat/0601225] [INSPIRE].
G. Mandal, R. Sinha and N. Sorokhaibam, Thermalization with chemical potentials, and higher spin black holes, JHEP 08 (2015) 013 [arXiv:1501.04580] [INSPIRE].
J. Cardy, Quantum Quenches to a Critical Point in One Dimension: some further results, J. Stat. Mech. 1602 (2016) 023103 [arXiv:1507.07266] [INSPIRE].
S. Sotiriadis and P. Calabrese, Validity of the GGE for quantum quenches from interacting to noninteracting models, J. Stat. Mech. 2014 (2014) P07024.
S. Sotiriadis, Memory-preserving equilibration after a quantum quench in a one-dimensional critical model, Phys. Rev. A 94 (2016) 031605 [arXiv:1507.07915] [INSPIRE].
M. Collura, S. Sotiriadis and P. Calabrese, Equilibration of a tonks-girardeau gas following a trap release, Phys. Rev. Lett. 110 (2013) 245301.
M. Collura, M. Kormos and P. Calabrese, Quantum quench in a harmonically trapped one-dimensional bose gas, Phys. Rev. A 97 (2018) 033609.
P. Ruggiero, Y. Brun and J. Dubail, Conformal field theory on top of a breathing one-dimensional gas of hard core bosons, SciPost Phys. 6 (2019) 51.
S.R. Das, D.A. Galante and R.C. Myers, Quantum Quenches in Free Field Theory: Universal Scaling at Any Rate, JHEP 05 (2016) 164 [arXiv:1602.08547] [INSPIRE].
S.R. Das, S. Hampton and S. Liu, Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory, JHEP 08 (2019) 176 [arXiv:1903.07682] [INSPIRE].
S.R. Das, D.A. Galante and R.C. Myers, Universality in fast quantum quenches, JHEP 02 (2015) 167 [arXiv:1411.7710] [INSPIRE].
S. Sotiriadis, G. Takács and G. Mussardo, Boundary State in an Integrable Quantum Field Theory Out of Equilibrium, Phys. Lett. B 734 (2014) 52 [arXiv:1311.4418] [INSPIRE].
G. Mandal, S. Paranjape and N. Sorokhaibam, Thermalization in 2D critical quench and UV/IR mixing, JHEP 01 (2018) 027 [arXiv:1512.02187] [INSPIRE].
S. Sotiriadis, D. Fioretto and G. Mussardo, Zamolodchikov-Faddeev algebra and quantum quenches in integrable field theories, J. Stat. Mech. 2012 (2012) P02017.
D.X. Horvath, S. Sotiriadis and G. Takács, Initial states in integrable quantum field theory quenches from an integral equation hierarchy, Nucl. Phys. B 902 (2016) 508 [arXiv:1510.01735] [INSPIRE].
B. Bertini, L. Piroli and P. Calabrese, Quantum quenches in the sinh-gordon model: steady state and one-point correlation functions, J. Stat. Mech. 2016 (2016) 063102.
A.C. Cubero, Planar quantum quenches: computation of exact time-dependent correlation functions at largeN, J. Stat. Mech. 2016 (2016) 083107.
V.E. Korepin, N.M. Bogoliubov and A.G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Monographs on Mathematical Physics, Cambridge University Press (1993).
S. Sotiriadis and J. Cardy, Quantum quench in interacting field theory: A Self-consistent approximation, Phys. Rev. B 81 (2010) 134305 [arXiv:1002.0167] [INSPIRE].
A. Chiocchetta, M. Tavora, A. Gambassi and A. Mitra, Short-time universal scaling and light-cone dynamics after a quench in an isolated quantum system in d spatial dimensions, Phys. Rev. B 94 (2016) 134311 [arXiv:1604.04614] [INSPIRE].
A. Chiocchetta, A. Gambassi, S. Diehl and J. Marino, Dynamical Crossovers in Prethermal Critical States, Phys. Rev. Lett. 118 (2017) 135701 [arXiv:1612.02419] [INSPIRE].
N. Birrell and P. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge University Press (1984).
S. Bhattacharyya et al., Currents and Radiation from the large D Black Hole Membrane, JHEP 05 (2017) 098 [arXiv:1611.09310] [INSPIRE].
A. Kaushal and G. Mandal, Approach to thermalization in bosonic O(N ) models in arbitrary dimensions, work in progress.
R.H. Jonsson, E. Martin-Martinez and A. Kempf, Information transmission without energy exchange, Phys. Rev. Lett. 114 (2015) 110505 [arXiv:1405.3988] [INSPIRE].
A. Blasco, L.J. Garay, M. Martin-Benito and E. Martin-Martinez, Violation of the Strong Huygen’s Principle and Timelike Signals from the Early Universe, Phys. Rev. Lett. 114 (2015) 141103 [arXiv:1501.01650] [INSPIRE].
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ArXiv ePrint: 1910.02404
Work started during a research project in TIFR (Parijat Banerjee).
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Banerjee, P., Gaikwad, A., Kaushal, A. et al. Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect. J. High Energ. Phys. 2020, 27 (2020). https://doi.org/10.1007/JHEP09(2020)027
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DOI: https://doi.org/10.1007/JHEP09(2020)027