We study a composite quantum quench of the energy gap and the interactions in the interacting ${\ensuremath{\phi}}^{4}$ model using a self-consistent approximation. First we review results for free theories where a quantum quench of the energy gap or mass leads for long times to stationary behavior with thermal characteristics. An exception to this rule is the $2d$ case with zero mass after the quench. In the composite quench, however, we find that the effect of the interactions in our approximation is simply to effectively change the value of the mass. This means on the one hand that the interacting model also exhibits the same stationary behavior and on the other hand that this is now true even for the massless $2d$ case.We study a composite quantum quench of the energy gap and the interactions in the interacting ${\ensuremath{\phi}}^{4}$ model using a self-consistent approximation. First we review results for free theories where a quantum quench of the energy gap or mass leads for long times to stationary behavior with thermal characteristics. An exception to this rule is the $2d$ case with zero mass after the quench. In the composite quench, however, we find that the effect of the interactions in our approximation is simply to effectively change the value of the mass. This means on the one hand that the interacting model also exhibits the same stationary behavior and on the other hand that this is now true even for the massless $2d$ case.

arXiv:1002.0167Physical Review BApr 30, 2010151 citations

Concentration quenching in exchange energy sinks

Anatoly I. Burshtein, Leonid D. Zusman

OptSpMay 1, 19750 citations

A new approach to the quenched bond-diluted Ising model

Eduardo Lage

The techniques developed by Edwards and Anderson (1975) for the spin-glass problem are here applied to the bond-diluted quenched Ising model (S= 1 / 2 ). The n to 0 trick is used to express exactly the free energy in terms of a generalized Hamiltonian representing n different but coupled replicas. The only approximation of the theory consists of decoupling these replicas in a way that reduces the free energy of the diluted system to that of a pure system with renormalized, concentration-dependent parameters. To first order in the concentration of missing bonds the author obtains all the results previously derived by Harris (1974) using a cumulant expansion and which are exact in this limit. More generally, the theory allows a discussion of the concentration dependence of the critical temperature; in particular, the values deduced for the critical concentration agree rather well with those obtained exactly or through series expansions. The behaviour of the system near the transition is also studied and the critical exponents are found to be Fisher-renormalized.The techniques developed by Edwards and Anderson (1975) for the spin-glass problem are here applied to the bond-diluted quenched Ising model (S= 1 / 2 ). The n to 0 trick is used to express exactly the free energy in terms of a generalized Hamiltonian representing n different but coupled replicas. The only approximation of the theory consists of decoupling these replicas in a way that reduces the free energy of the diluted system to that of a pure system with renormalized, concentration-dependent parameters. To first order in the concentration of missing bonds the author obtains all the results previously derived by Harris (1974) using a cumulant expansion and which are exact in this limit. More generally, the theory allows a discussion of the concentration dependence of the critical temperature; in particular, the values deduced for the critical concentration agree rather well with those obtained exactly or through series expansions. The behaviour of the system near the transition is also studied and the critical exponents are found to be Fisher-renormalized.

Journal of Physics C Solid State PhysicsMar 14, 197712 citations

Critical phenomena and quenched disorder

Виктор Степанович Доценко

Uspekhi Fizicheskih NaukJan 1, 199580 citations

Quantum quenches in an interacting field theory: Full quantum evolution versus semiclassical approximations

D. Szász-Schagrin, Izabella Lovas, G. Takács

We develop a truncated Hamiltonian method to investigate the dynamics of the $(1+1)$ -dimensional ${\ensuremath{\phi}}^{4}$ theory following quantum quenches. The results are compared to two different semiclassical approaches, the self-consistent Gaussian approximation and the truncated Wigner approximation, and used to determine the range of validity of these widely used approaches. We show that the self-consistent approximation is strongly limited in comparison to the truncated Hamiltonian method which for larger cutoffs is practically exact for the parameter range studied. We find that the self-consistent approximation is only valid when the effective mass is in the vicinity of the renormalized mass. Similarly to the self-consistent approximation, the truncated Wigner approximation (TWA) is not able to capture the correct mass renormalization, and breaks down for strong enough interactions where the bare mass becomes negative. We attribute the failure of TWA to the presence of a classical symmetry-broken fixed point. Aside from establishing the truncated Hamiltonian approach as a powerful tool for studying the dynamics of the ${\ensuremath{\phi}}^{4}$ model, our results on the limitation of semiclassical approximations are expected to be relevant for modeling the dynamics of other quantum field theories.We develop a truncated Hamiltonian method to investigate the dynamics of the $(1+1)$-dimensional ${\ensuremath{\phi}}^{4}$ theory following quantum quenches. The results are compared to two different semiclassical approaches, the self-consistent Gaussian approximation and the truncated Wigner approximation, and used to determine the range of validity of these widely used approaches. We show that the self-consistent approximation is strongly limited in comparison to the truncated Hamiltonian method which for larger cutoffs is practically exact for the parameter range studied. We find that the self-consistent approximation is only valid when the effective mass is in the vicinity of the renormalized mass. Similarly to the self-consistent approximation, the truncated Wigner approximation (TWA) is not able to capture the correct mass renormalization, and breaks down for strong enough interactions where the bare mass becomes negative. We attribute the failure of TWA to the presence of a classical symmetry-broken fixed point. Aside from establishing the truncated Hamiltonian approach as a powerful tool for studying the dynamics of the ${\ensuremath{\phi}}^{4}$ model, our results on the limitation of semiclassical approximations are expected to be relevant for modeling the dynamics of other quantum field theories.

arXiv:2110.01636Physical review. B./Physical review. BJan 10, 202215 citations

2d

case with zero mass after the quench. In the composite quench, however, we find that the effect of the interactions in our approximation is simply to effectively change the value of the mass. This means on the one hand that the interacting model also exhibits the same stationary behavior and on the other hand that this is now true even for the massless

2d

case.

We develop a truncated Hamiltonian method to investigate the dynamics of the

(1+1)

-dimensional ${\ensuremath{\phi}}^{4}$ theory following quantum quenches. The results are compared to two different semiclassical approaches, the self-consistent Gaussian approximation and the truncated Wigner approximation, and used to determine the range of validity of these widely used approaches. We show that the self-consistent approximation is strongly limited in comparison to the truncated Hamiltonian method which for larger cutoffs is practically exact for the parameter range studied. We find that the self-consistent approximation is only valid when the effective mass is in the vicinity of the renormalized mass. Similarly to the self-consistent approximation, the truncated Wigner approximation (TWA) is not able to capture the correct mass renormalization, and breaks down for strong enough interactions where the bare mass becomes negative. We attribute the failure of TWA to the presence of a classical symmetry-broken fixed point. Aside from establishing the truncated Hamiltonian approach as a powerful tool for studying the dynamics of the ${\ensuremath{\phi}}^{4}$ model, our results on the limitation of semiclassical approximations are expected to be relevant for modeling the dynamics of other quantum field theories.