In this article, we study the quantum field theoretic generalization of the Caldeira-Leggett model in general curved space-time considering interactions between two scalar fields in a classical gravitational background. The thermalization phenomena is then studied from the obtained de Sitter solution using quantum quench from one scalar field model obtained from path integrated effective action. We consider an instantaneous quench in the time-dependent mass protocol of the field of our interest. We find that the dynamics of the field post-quench can be described in terms of the state of the generalized Calabrese-Cardy (gCC) form and computed the different types of two-point correlation functions in this context. We explicitly found the conserved charges of algebra that represents the gCC state after a quench in de Sitter space and found it to be significantly different from the flat space-time results. We extend our study for the different two-point correlation functions not only considering the pre-quench state as the ground state, but also a squeezed state. We found that irrespective of the pre-quench state, the post quench state can be written in terms of the gCC state showing that the subsystem of our interest thermalizes in de Sitter space. Furthermore, we provide a general expression for the two-point correlators and explicitly show the thermalization process by considering a thermal Generalized Gibbs ensemble (GGE). Finally, from the equal time momentum dependent counterpart of the obtained results for the two-point correlators, we have studied the hidden features of the power spectra and studied its consequences for different choices of the quantum initial conditions.In this article, we study the quantum field theoretic generalization of the Caldeira-Leggett model in general curved space-time considering interactions between two scalar fields in a classical gravitational background. The thermalization phenomena is then studied from the obtained de Sitter solution using quantum quench from one scalar field model obtained from path integrated effective action. We consider an instantaneous quench in the time-dependent mass protocol of the field of our interest. We find that the dynamics of the field post-quench can be described in terms of the state of the generalized Calabrese-Cardy (gCC) form and computed the different types of two-point correlation functions in this context. We explicitly found the conserved charges of algebra that represents the gCC state after a quench in de Sitter space and found it to be significantly different from the flat space-time results. We extend our study for the different two-point correlation functions not only considering the pre-quench state as the ground state, but also a squeezed state. We found that irrespective of the pre-quench state, the post quench state can be written in terms of the gCC state showing that the subsystem of our interest thermalizes in de Sitter space. Furthermore, we provide a general expression for the two-point correlators and explicitly show the thermalization process by considering a thermal Generalized Gibbs ensemble (GGE). Finally, from the equal time momentum dependent counterpart of the obtained results for the two-point correlators, we have studied the hidden features of the power spectra and studied its consequences for different choices of the quantum initial conditions.

arXiv:2104.10692Apr 21, 20211 citation

Thermalization Phenomena in Quenched Quantum Brownian Motion in De Sitter Space

Subhashish Banerjee, Sayantan Choudhury, Satyaki Chowdhury +3 more

In this article, we study the quantum field theoretic generalization of the Caldeira-Leggett model to describe the Brownian Motion in general curved space-time considering interactions between two scalar fields in a classical gravitational background. The thermalization phenomena is then studied from the obtained de Sitter solution using quantum quench from one scalar field model obtained from path integrated effective action in Euclidean signature. We consider an instantaneous quench in the time-dependent mass protocol of the field of our interest. We find that the dynamics of the field post-quench can be described in terms of the state of the generalized Calabrese-Cardy (gCC) form and computed the different types of two-point correlation functions in this context. We explicitly found the conserved charges of W∞ algebra that represents the gCC state after a quench in de Sitter space and found it to be significantly different from the flat space-time results. We extend our study for the different two-point correlation functions not only considering the pre-quench state as the ground state, but also a squeezed state. We found that irrespective of the pre-quench state, the post quench state can be written in terms of the gCC state showing that the subsystem of our interest thermalizes in de Sitter space. Furthermore, we provide a general expression for the two-point correlators and explicitly show the thermalization process by considering a thermal Generalized Gibbs ensemble (GGE). Finally, from the equal time momentum dependent counterpart of the obtained results for the two-point correlators, we have studied the hidden features of the power spectra and studied its consequences for different choices of the quantum initial conditions.In this article, we study the quantum field theoretic generalization of the Caldeira-Leggett model to describe the Brownian Motion in general curved space-time considering interactions between two scalar fields in a classical gravitational background. The thermalization phenomena is then studied from the obtained de Sitter solution using quantum quench from one scalar field model obtained from path integrated effective action in Euclidean signature. We consider an instantaneous quench in the time-dependent mass protocol of the field of our interest. We find that the dynamics of the field post-quench can be described in terms of the state of the generalized Calabrese-Cardy (gCC) form and computed the different types of two-point correlation functions in this context. We explicitly found the conserved charges of W∞ algebra that represents the gCC state after a quench in de Sitter space and found it to be significantly different from the flat space-time results. We extend our study for the different two-point correlation functions not only considering the pre-quench state as the ground state, but also a squeezed state. We found that irrespective of the pre-quench state, the post quench state can be written in terms of the gCC state showing that the subsystem of our interest thermalizes in de Sitter space. Furthermore, we provide a general expression for the two-point correlators and explicitly show the thermalization process by considering a thermal Generalized Gibbs ensemble (GGE). Finally, from the equal time momentum dependent counterpart of the obtained results for the two-point correlators, we have studied the hidden features of the power spectra and studied its consequences for different choices of the quantum initial conditions.

Apr 21, 20212 citations

Thermalization in 2D critical quench and UV/IR mixing

Gautam Mandal, Shruti Paranjape, Nilakash Sorokhaibam

We consider quantum quenches in models of free scalars and fermions with a generic time-dependent mass m(t) that goes from m0 to zero. We prove that, as anticipated in MSS [1], the post-quench dynamics can be described in terms of a state of the generalized Calabrese-Cardy form |ψ〉 = exp[−κ2H − ∑ >2 ∞ κ n W n ]|Bd〉. The W n (n = 2, 3, . . ., W2 = H) here represent the conserved W∞ charges and |Bd〉 represents a conformal boundary state. Our result holds irrespective of whether the pre-quench state is a ground state or a squeezed state, and is proved without recourse to perturbation expansion in the κ n ’s as in MSS. We compute exact time-dependent correlators for some specific quench protocols m(t). The correlators explicitly show thermalization to a generalized Gibbs ensemble (GGE), with inverse temperature β = 4κ2, and chemical potentials μ n = 4κ n . In case the pre-quench state is a ground state, it is possible to retrieve the exact quench protocol m(t) from the final GGE, by an application of inverse scattering techniques. Another notable result, which we interpret as a UV/IR mixing, is that the long distance and long time (IR) behaviour of some correlators depends crucially on all κ n ’s, although they are highly irrelevant couplings in the usual RG parlance. This indicates subtleties in RG arguments when applied to non-equilibrium dynamics.We consider quantum quenches in models of free scalars and fermions with a generic time-dependent mass m(t) that goes from m0 to zero. We prove that, as anticipated in MSS [1], the post-quench dynamics can be described in terms of a state of the generalized Calabrese-Cardy form |ψ〉 = exp[−κ2H − ∑ >2 ∞ κ n W n ]|Bd〉. The W n (n = 2, 3, . . ., W2 = H) here represent the conserved W∞ charges and |Bd〉 represents a conformal boundary state. Our result holds irrespective of whether the pre-quench state is a ground state or a squeezed state, and is proved without recourse to perturbation expansion in the κ n ’s as in MSS. We compute exact time-dependent correlators for some specific quench protocols m(t). The correlators explicitly show thermalization to a generalized Gibbs ensemble (GGE), with inverse temperature β = 4κ2, and chemical potentials μ n = 4κ n . In case the pre-quench state is a ground state, it is possible to retrieve the exact quench protocol m(t) from the final GGE, by an application of inverse scattering techniques. Another notable result, which we interpret as a UV/IR mixing, is that the long distance and long time (IR) behaviour of some correlators depends crucially on all κ n ’s, although they are highly irrelevant couplings in the usual RG parlance. This indicates subtleties in RG arguments when applied to non-equilibrium dynamics.

Journal of High Energy PhysicsJan 1, 201829 citations

Thermalization in 2D critical quench and UV/IR mixing

Gautam Mandal, Shruti Paranjape, Nilakash Sorokhaibam

We consider quantum quenches in models of free scalars and fermions with a generic time-dependent mass $m(t)$ that goes from $m_0$ to zero. We prove that, as anticipated in MSS \cite{Mandal:2015jla}, the post-quench dynamics can be described in terms of a state of the generalized Calabrese-Cardy form $|ψ\rangle$ = $\exp[-κ_2 H -\sum_{n>2}^\infty κ_n W_n]| \hbox{Bd} \rangle$ . The $W_n$ ( $n=2,3,...$ , $W_2=H$ ) here represent the conserved $W_\infty$ charges and $| \hbox{Bd} \rangle$ represents a conformal boundary state. Our result holds irrespective of whether the pre-quench state is a ground state or a squeezed state, and is proved without recourse to perturbation expansion in the $κ_n$ 's as in MSS. We compute exact time-dependent correlators for some specific quench protocols $m(t)$ . The correlators explicitly show thermalization to a generalized Gibbs ensemble (GGE), with inverse temperature $β= 4κ_2$ , and chemical potentials $μ_n=4κ_n$ . In case the pre-quench state is a ground state, it is possible to retrieve the exact quench protocol $m(t)$ from the final GGE, by an application of inverse scattering techniques. Another notable result, which we interpret as a UV/IR mixing, is that the long distance and long time (IR) behaviour of some correlators depends crucially on all $κ_n$ 's, although they are highly irrelevant couplings in the usual RG parlance. This indicates subtleties in RG arguments when applied to non-equilibrium dynamics.We consider quantum quenches in models of free scalars and fermions with a generic time-dependent mass $m(t)$ that goes from $m_0$ to zero. We prove that, as anticipated in MSS \cite{Mandal:2015jla}, the post-quench dynamics can be described in terms of a state of the generalized Calabrese-Cardy form $|ψ\rangle$= $\exp[-κ_2 H -\sum_{n>2}^\infty κ_n W_n]| \hbox{Bd} \rangle$. The $W_n$ ($n=2,3,...$, $W_2=H$) here represent the conserved $W_\infty$ charges and $| \hbox{Bd} \rangle$ represents a conformal boundary state. Our result holds irrespective of whether the pre-quench state is a ground state or a squeezed state, and is proved without recourse to perturbation expansion in the $κ_n$'s as in MSS. We compute exact time-dependent correlators for some specific quench protocols $m(t)$. The correlators explicitly show thermalization to a generalized Gibbs ensemble (GGE), with inverse temperature $β= 4κ_2$, and chemical potentials $μ_n=4κ_n$. In case the pre-quench state is a ground state, it is possible to retrieve the exact quench protocol $m(t)$ from the final GGE, by an application of inverse scattering techniques. Another notable result, which we interpret as a UV/IR mixing, is that the long distance and long time (IR) behaviour of some correlators depends crucially on all $κ_n$'s, although they are highly irrelevant couplings in the usual RG parlance. This indicates subtleties in RG arguments when applied to non-equilibrium dynamics.

arXiv:1512.02187Dec 7, 20154 citations

Quantum quench from a thermal tensor state: Boundary effects and generalized Gibbs ensemble

Mario Collura, Dragi Karevski

We consider a quantum quench in a noninteracting fermionic one-dimensional field theory. The system of size $L$ is initially prepared into two halves $\mathcal{L}$ $([\ensuremath{-}L/2,0])$ and $\mathcal{R}$ $([0,L/2])$ , each of them thermalized at two different temperatures ${T}_{\mathcal{L}}$ and ${T}_{\mathcal{R}}$ , respectively. At a given time, the two halves are joined together by a local coupling and the whole system is left to evolve unitarily. For an infinitely extended system $(L\ensuremath{\rightarrow}\ensuremath{\infty})$, we show that the time evolution of the particle and energy densities is well described via a hydrodynamic approach which allows us to evaluate the correspondent stationary currents. We show, in such a case, that the two-point correlation functions are deduced, at large times, from a simple nonequilibrium steady state. Otherwise, whenever the boundary conditions are retained (in a properly defined thermodynamic limit), any current is suppressed at large times, and the stationary state is described by a generalized Gibbs ensemble, which is diagonal and depends only on the post-quench mode occupation.We consider a quantum quench in a noninteracting fermionic one-dimensional field theory. The system of size $L$ is initially prepared into two halves $\mathcal{L}$ $([\ensuremath{-}L/2,0])$ and $\mathcal{R}$ $([0,L/2])$, each of them thermalized at two different temperatures ${T}_{\mathcal{L}}$ and ${T}_{\mathcal{R}}$, respectively. At a given time, the two halves are joined together by a local coupling and the whole system is left to evolve unitarily. For an infinitely extended system $(L\ensuremath{\rightarrow}\ensuremath{\infty})$, we show that the time evolution of the particle and energy densities is well described via a hydrodynamic approach which allows us to evaluate the correspondent stationary currents. We show, in such a case, that the two-point correlation functions are deduced, at large times, from a simple nonequilibrium steady state. Otherwise, whenever the boundary conditions are retained (in a properly defined thermodynamic limit), any current is suppressed at large times, and the stationary state is described by a generalized Gibbs ensemble, which is diagonal and depends only on the post-quench mode occupation.

arXiv:1402.1944Physical Review BJun 30, 201494 citations

Thermalization and non-monotonic entanglement growth in an exactly solvable model

Shruti Paranjape, Nilakash Sorokhaibam

Abstract We study quantum quenches and subsequent non-equilibrium dynamics of free Dirac fermions in 1 + 1 spacetime dimensions using time dependent mass. The final state is a normalized boundary state which is called generalized Calabrese-Cardy (gCC) state and the system thermalizes to a generalized Gibb’s Ensemble(GGE). We can also tune the initial states so that the final states are exact Calabrese-Cardy (CC) state and special gCC states. The system in the CC state thermalizes to a Gibb’s ensemble. We derive closed-form analytic expressions for the growth of entanglement entropy of subsystems consisting of arbitrary number of disjoint intervals in CC state. We show that the entanglement entropy of a single interval grows monotonically before saturation. In case of certain gCC states, for particular charges, the entanglement entropy of a single interval grows non-monotonically when the effective chemical potential is increased beyond a critical value. We argue that the non-monotonic growth of entanglement entropy is a boundary effect which arises due to increase in long range correlation and decrease in short range correlation at early times.Abstract We study quantum quenches and subsequent non-equilibrium dynamics of free Dirac fermions in 1 + 1 spacetime dimensions using time dependent mass. The final state is a normalized boundary state which is called generalized Calabrese-Cardy (gCC) state and the system thermalizes to a generalized Gibb’s Ensemble(GGE). We can also tune the initial states so that the final states are exact Calabrese-Cardy (CC) state and special gCC states. The system in the CC state thermalizes to a Gibb’s ensemble. We derive closed-form analytic expressions for the growth of entanglement entropy of subsystems consisting of arbitrary number of disjoint intervals in CC state. We show that the entanglement entropy of a single interval grows monotonically before saturation. In case of certain gCC states, for particular charges, the entanglement entropy of a single interval grows non-monotonically when the effective chemical potential is increased beyond a critical value. We argue that the non-monotonic growth of entanglement entropy is a boundary effect which arises due to increase in long range correlation and decrease in short range correlation at early times.

arXiv:1609.02926The European Physical Journal CDec 19, 20242 citations

We consider quantum quenches in models of free scalars and fermions with a generic time-dependent mass

m(t)

that goes from

m_0

to zero. We prove that, as anticipated in MSS \cite{Mandal:2015jla}, the post-quench dynamics can be described in terms of a state of the generalized Calabrese-Cardy form

|ψ\rangle

\exp[-κ_2 H -\sum_{n>2}^\infty κ_n W_n]| \hbox{Bd} \rangle

. The

W_n

(

n=2,3,...

W_2=H

) here represent the conserved

W_\infty

charges and

| \hbox{Bd} \rangle

represents a conformal boundary state. Our result holds irrespective of whether the pre-quench state is a ground state or a squeezed state, and is proved without recourse to perturbation expansion in the

κ_n

's as in MSS. We compute exact time-dependent correlators for some specific quench protocols

m(t)

. The correlators explicitly show thermalization to a generalized Gibbs ensemble (GGE), with inverse temperature

β= 4κ_2

, and chemical potentials

μ_n=4κ_n

. In case the pre-quench state is a ground state, it is possible to retrieve the exact quench protocol

m(t)

from the final GGE, by an application of inverse scattering techniques. Another notable result, which we interpret as a UV/IR mixing, is that the long distance and long time (IR) behaviour of some correlators depends crucially on all

κ_n

's, although they are highly irrelevant couplings in the usual RG parlance. This indicates subtleties in RG arguments when applied to non-equilibrium dynamics.

We consider a quantum quench in a noninteracting fermionic one-dimensional field theory. The system of size

L

is initially prepared into two halves

\mathcal{L}

$([\ensuremath{-}L/2,0])$ and

\mathcal{R}

([0,L/2])

, each of them thermalized at two different temperatures

{T}_{\mathcal{L}}

and

{T}_{\mathcal{R}}

, respectively. At a given time, the two halves are joined together by a local coupling and the whole system is left to evolve unitarily. For an infinitely extended system $(L\ensuremath{\rightarrow}\ensuremath{\infty})$, we show that the time evolution of the particle and energy densities is well described via a hydrodynamic approach which allows us to evaluate the correspondent stationary currents. We show, in such a case, that the two-point correlation functions are deduced, at large times, from a simple nonequilibrium steady state. Otherwise, whenever the boundary conditions are retained (in a properly defined thermodynamic limit), any current is suppressed at large times, and the stationary state is described by a generalized Gibbs ensemble, which is diagonal and depends only on the post-quench mode occupation.