Thermo Field Dynamics Formalism Research Articles

On Fermion-Graviton Scattering at Finite Temperature

The early universe is dominated by phenomena at high temperatures. The thermal effects decrease during evolution of the universe. However there are some phenomena, such as processes inside stars and black holes, where the role of the temperature is important. Study of processes involving gravitons at finite temperature is a viable means to understand gravitational processes in the universe. Using the Thermo Field Dynamics formalism transition amplitudes involving gravitons and fermions at finite temperature are calculated. In this approach our results consist of two parts: one corresponding to the zero temperature part and the other corresponding to a temperature dependent part.

Entanglement of higher-derivative oscillators in holographic systems

We study the quantum entanglement of coupled Pais–Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of N coupled Pais–Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.

Aether field in extra dimensions: Stefan-Boltzmann law and Casimir effect at finite temperature

The Lorentz and $CPT$ symmetries are not violated at the highest laboratory energies available. However these symmetries may be violated at Planck scale. A particular development is to investigate the breakdown of Lorentz and $CPT$ symmetries by introducing an aether field that exhibits nonzero vacuum expectation value along the fifth dimension. The interactions of the aether field with scalar, electromagnetic, and fermions fields are analyzed. The Stefan-Boltzmann law and Casimir effect at finite temperature are calculated using the Thermo Field Dynamics formalism.

Neutrino Processes with Hot Nuclei in Supernovae

In this paper, we calculate cross sections for charged-current neutrino-nucleus processes occuring under presupernova conditions. To treat thermal effects we extend self-consistent Skyrme-QRPA calculations to finite temperature by using the formalism of thermo field dynamics. The numerical results are presented for the sample nuclei, $^{56}$Fe and $^{82}$Ge

Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space

The two-dimensional σ-model with the de Sitter target space is locally canonic in the north pole diamond of the Penrose diagram in the cosmological gauge. The left and right moving modes on the cylindrical base space are entangled among themselves and interact with the de Sitter metric. Firstly, we show that the untangled oscillators can be obtained from the entangled operators by applying a set of Bogoliubov transformations constrained by the requirement that the partial evolution generator be diagonal. Secondly, we determine the nonequilibrium dynamics of the untangled modes in the nonequilibrium thermofield dynamics formalism. The thermal modes are represented as thermal doublet oscillators that satisfy partial evolution equations of Heisenberg-type. From these we compute the local free one-body propagator of an arbitrary mode between two times. Thirdly, we discuss the field representation of the thermal modes. We show that there is a set of thermal doublet fields that satisfy the equal time canonical commutation relations, are solutions to the σ-model equations of motion, and can be decomposed in terms of thermal doublet oscillators. Finally, we construct a local partial evolution functional of Hamilton-like form for the thermal doublet fields.

Standard Model Extension and Casimir effect for fermions at finite temperature

Abstract Lorentz and CPT symmetries are foundations for important processes in particle physics. Recent studies in Standard Model Extension (SME) at high energy indicate that these symmetries may be violated. Modifications in the lagrangian are necessary to achieve a hermitian hamiltonian. The fermion sector of the standard model extension is used to calculate the effects of the Lorentz and CPT violation on the Casimir effect at zero and finite temperature. The Casimir effect and Stefan–Boltzmann law at finite temperature are calculated using the thermo field dynamics formalism.

The Master Equation for Two-Level Accelerated Systems at Finite Temperature

In this work we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a \emph{reservoir} in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a \emph{reservoir}, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.

Neutrino-nucleus reactions in supernovae

We study thermal effects on neutrino-nucleus reactions occurring under supernova conditions. The approach we use is based on the QRPA extended to finite temperature by the thermofield dynamics formalism. For the relevant supernova conditions we calculate inelastic neutrino scattering and neutrino absorption cross sections for two sample nuclei, 56 Fe and 82 Ge. In addition, we apply the approach to examine the rate of neutrino-antineutrino pair emission by hot nuclei.

Relation between the usual and the entanglement temperature, in a simple quantum system

We develop a thermodynamical theory to describe the behavior of the entanglement between a single two-level atom with a single mode of the electromagnetic field. The resonant Jaynes–Cummings model is used to study both the entanglement thermodynamics, in particular the entanglement temperature, and its connection with the average number of photons in the optical cavity. We find that this entanglement temperature has a strong dependence with the initial conditions of the atom. We show that the entanglement temperature between the photons and the atom defined in this work is the same temperature obtained within the Jaynes–Cummings model at finite temperature developed in the Thermo-Field Dynamics formalism.

On finite-temperature string field theory and p-adic string

Covariant string field theory at finite temperature using quantum double (thermofield dynamics) formalism is considered. Thermal p-adic string theory amplitudes and a natural generalization of p-adic string effective action to the case on non-zero temperature are proposed.

Beyond the Schwinger boson representation of the su(2)-algebra

With the use of two kinds of boson operators, a new boson representation of the su(2)-algebra is proposed. The basic idea comes from the pseudo su(1,1)-algebra recently given by the present authors. It forms a striking contrast to the Schwinger boson representation of the su(2)-algebra which is also based on two kinds of bosons. This representation may be suitable for describing time-dependence of the system interacting with the external environment in the framework of the thermo field dynamics formalism, i.e., the phase space doubling. Further, several deformations related to the su(2)-algebra in this boson representation are discussed. On the basis of these deformed algebra, various types of time-evolution of a simple boson system are investigated.

Quantum Entanglement in Coupled Lossy Waveguides Using SU(2) and SU(1, 1) Thermo-Algebras

In this paper, the master equation for the coupled lossy waveguides is solved using the thermofield dynamics (TFD) formalism. This formalism allows the use of the underlying symmetry algebras SU(2) and SU(1, 1), associated with the Hamiltonian of the coupled lossy waveguides, to compute entanglement and decoherence as a function of time for various input states such as NOON states and thermal states.

Quantum Entanglement in Coupled Lossy Waveguides Using SU(2) and SU(1, 1) Thermo-Algebras

In this paper, the master equation for the coupled lossy waveguides is solved using the thermofield dynamics(TFD) formalism. This formalism allows the use of the underlying symmetry algebras SU(2) and SU(1,1), associated with the Hamiltonian of the coupled lossy waveguides,to compute entanglement and decoherence as a function of time for various input states such as NOON states and thermal states.

Neutrino-antineutrino pair emission from thermally excited nuclei in stellar collapse

We examine the rate of neutrino-antineutrino pair emission by hot nuclei in collapsing stellar cores. The rates are calculated assuming that only allowed charge-neutral Gamow-Teller (GT$_0$) transitions contribute to the decay of thermally excited nuclear states. To obtain the GT$_0$ transition matrix elements, we employ the quasiparticle random phase approximation extended to finite temperatures within the thermo field dynamics formalism. The decay rates and the energy emission rates are calculated for the sample nuclei ${}^{56}$Fe and $^{82}$Ge at temperatures relevant to core collapse supernovae.

A pseudo su(1,1)-algebraic deformation of the Cooper pair in the su(2)-algebraic many-fermion model

A pseudo su(1,1)-algebra is formulated as a possible deformation of the Cooper-pair in the su(2)-algebraic many-fermion system. With the aid of this algebra, it is possible to describe behavior of individual fermions which are generated as the result of interaction with the external environment. The form presented in this paper is a generalization of a certain simple case developed recently by the present authors. Basic idea follows the su(1,1)-algebra in the Schwinger boson representation for treating energy transfer between the harmonic oscillator and the external environment. Hamiltonian is given under the idea of the phase space doubling in the thermo-field dynamics formalism and the time-dependent variational method is applied to this Hamiltonian. Its trial state is constructed in the frame deformed from the BCS-Bogoliubov approach to the superconductivity. Several numerical results are shown.

Thermalizing Quantum Correlations in Two-Atom System

We derive the phenomena of thermalizing quantum correlations (including the entanglement, quantum discord and the consonance) in a system composed of two atoms. Making use of the thermo field dynamics formalism, we investigate finite temperature field effects on the results of thermalization.

Tensor network and a black hole

A tensor network formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, multiscale entanglement renormalization anzats (MERA) reproduces an AdS black hole at finite temperature. Our finding shows rich functionalities of MERA as efficient graphical representation of AdS/CFT correspondence.

String in AdS black hole: A thermo field dynamic approach

Based on Maldacena's description of an eternal AdS-black hole, we reassess the Thermo Field Dynamics (TFD) formalism in the context of the AdS/CFT correspondence. The model studied here involves the maximally extended AdS-Schwarschild solution and two (non-interacting) copies of the CFT associated to the global AdS spacetime, along with an extension of the string by imposing natural gluing conditions in the horizon. We show that the gluing conditions in the horizon define a string boundary state which is identified with the TFD thermal vacuum, globally defined in the Kruskal extension of the AdS black hole. We emphasize the connection of this picture with unitary SU(1,1) TFD formulation and we show that information about the bulk and the conformal boundary is present in the SU(1,1) parameters. Using the unitary SU(1,1) TFD formulation, a canonical prescription for calculating the worldsheet real time thermal Green's function is made and the entropy associated with the entanglement of the two CFT's is calculated.

Finite Temperature Master Equation

We study the behavior of two weakly coupled quantum systems, described by a separable density operator. One of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators, which perform the role of a reservoir in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism and suitably redefining the vacuum of the macroscopic system. As applications, we study an oscillator interacting with a set of boson oscillators at finite temperature, usually employed in quantum mechanics to describe a Brownian particle; and investigate the behavior of an oscillator in the presence of a heat bath consisting of a set of fermion oscillators.

NO-CLONING THEOREM IN THERMOFIELD DYNAMICS

We discuss the relation between the no-cloning theorem from quantum information and the doubling procedure used in the formalism of thermofield dynamics (TFD). We also discuss how to apply the no-cloning theorem in the context of thermofield states defined in TFD. Consequences associated to mixed states, von Neumann entropy and thermofield vacuum are also addressed.