Thermo Field Dynamics Research Articles

An Analysis of the Thermal Behavior and Effects of Circular Quartz Crystal Resonators for Microbalance Applications.

The accurate calculation of vibration frequency is essential in design of circular quartz crystal resonators which are the core elements of high-precision microbalances used for testing and measurement. Currently, the prediction of thermal effects on frequency through an analytical analysis is still in its developmental stage, mainly due to the complexity of solving the 3-D equations with the consideration of asymmetric structure of resonators and electrodes along with material anisotropy. By using a scalar differential equation for vibrations with the eigen-displacement of thickness mode, the eigen-frequency of a plano-convex AT-cut circular quartz crystal plate with asymmetric electrodes is determined. Furthermore, the temperature effect in the scalar differential equation is successfully obtained by incorporating the incremental thermal field theory into the 1-D analysis. The theoretical results agree well with the experimental data. The combination of the thermal field and the thickness model for circular quartz crystal resonators can realize a full analysis of thermal properties in vital applications such as high-sensitivity microbalance sensors.

Meson scattering in a Lorentz-violating scalar QED at finite temperature

This paper investigates how the nonzero temperature affects the differential cross-section for mesons scattering in a Lorentz-violating extension of the scalar electrodynamics. We initially discuss some features of the model and extract the zero temperature Feynman rules. Temperature effects are introduced using the Thermo Field Dynamics (TFD) formalism. It is shown that the corrections induced on the meson scattering are very large in the high-temperature regime. Furthermore, our results also suggest that temperature effects may contribute to new constraints on the Lorentz-violating parameters.

Quasinormal modes of NUT-charged black branes in the AdS/CFT correspondence

We study the scalar, electromagnetic and gravitational perturbations of planar AdS4 black holes with NUT charge. In the context of the AdS/CFT correspondence, these solutions describe a thermal quantum field theory embedded in a Gödel-type Universe with closed time-like curves. For a given temperature and NUT charge, two different planar Taub–NUT solutions exist, but we show that only the one with a positive specific heat contributes to the Euclidean saddle point in the path integral. By using the Newman–Penrose formalism, we then derive the master equations satisfied by scalar, electromagnetic and gravitational perturbations in this background, and show that the corresponding equations are separable. Interestingly, the solutions pile up in the form of Landau levels, and hence are characterized by a single quantum number q. We determine the appropriate boundary conditions satisfied by the master variables and using these we compute the quasinormal modes of scalar and gravitational perturbations. On the other hand, electromagnetic perturbations depend on a free parameter whose determination is problematic. We find that all the scalar and gravitational QNM frequencies lie in the lower half of the complex plane, indicating that these Taub–NUT spacetimes are stable. We discuss the implications of these results in the light of the AdS/CFT correspondence.

Real-time thermal self-energies: In the variational bases and spaces

In this work, we introduce a systematic study for studying the scalar propagator and tadpole self-energy by considering an arbitrary parameter σ that allows for a path integral description in real-time formalism (RTF). The closed time path formalism (CTP) and Thermofield Dynamics (TFD) are two popular choices for the parameter σ in the Feynman rules. We have constructed a scalar propagator and a tadpole self-energy in two different bases in the momentum space as well as the mixed space. The results show that the diagonal components of self-energy in both spaces for the 1/2 basis are the same in both approaches within RTF, whereas the other off-diagonal components of self-energy are different because they depend on the path parameter. On the other hand, the diagonal components of self-energy in both spaces for the new basis are not the same in both approaches within RTF, whereas the off-diagonal components of self-energy are vanishing. That means the new basis allows one to reduce the components for the quantities studied, like self-energy or other.

Vacuum Cherenkov radiation at finite temperature

In this paper we examine the thermal effects of the vacuum Cherenkov radiation in a Lorentz- and CPT-violating electrodynamics. We compute the thermal contribution to the Cherenkov radiation rate within the Thermofield Dynamics approach. Since the model under consideration possesses a consistent canonical quantization and also fulfills the physical constraints in order to this vacuum process to happen, it is a perfect candidate to implement the study at finite temperature. We evaluate in details the instantaneous rate of energy loss for a charge, and show that the radiation rate is significantly modified at very high temperatures. Intriguingly, we further observe that when the temperature goes to infinity the radiation rate goes to zero even if the process is kinematically allowed.

Electromagnetic spectral functions in hot and dense chirally imbalanced quark matter

The photon self-energy from chirally imbalanced quark matter is evaluated at finite temperature and density using the real time formulation of thermal field theory. The analytic structure is explored in detail exposing the cut structure which corresponds to a variety of physical scattering and decay processes in the medium and their thresholds. The mass of the quarks in the chiral symmetry broken phase are obtained from the gap equation of the Nambu--Jona-Lasinio model. It is found that, in presence of finite chiral chemical potential, the chiral condensate tends to get stronger at low temperatures while the opposite is observed at high temperature values. A continuous spectrum is obtained for the electromagnetic spectral function and this is purely a finite chiral chemical potential effect.

Dissipation process in eternal black holes

We consider the effect of the double trace deformation on the eternal black hole. On the boundary CFTs, the deformation can be considered the dissipation in the thermofield dynamics framework. In this framework, the entanglement operator describes the dissipation effect in boundary CFT. Corresponding to CFTs, the wormhole in spacetime and the defect in code subspace are formed as dissipative structures. These dissipative structures realize efficient processing through hierarchical information in the gravitational system. Further, the Fisher information metric renders the Lyapunov functional, which gives a criterion for the stability of the eternal black hole.

Single-particle spectra in relativistic heavy-ion collisions within the thermal quantum field theory

Abstract A quantum generalization of the Cooper–Frye recipe is proposed. The calculation of the single-particle spectrum arising in relativistic collisions of particles and nuclei is carried out within the framework of thermal quantum field theory. The starting point of consideration is the solution of the initial-value problem of the radiation of particles from a space-like hypersurface. In the next steps, we obtain a single-particle spectrum using the ‘lesser’ Green’s function associated with the fireball environment. Based on this result, several specific conditions for particle emission are considered.

Effective electromagnetic actions for Lorentz violating theories exhibiting the axial anomaly

The CPT odd contribution to the effective electromagnetic action deriving from the vacuum polarization tensor in a large class of fermionic systems exhibiting Lorentz invariance violation (LIV) is calculated using thermal field theory methods, focusing upon corrections depending on the chemical potential. The systems considered exhibit the axial anomaly and their effective actions are described by axion electrodynamics whereby all the LIV parameters enter in the coupling Θ(x) to the unmodified Pontryagin density. A preliminary application to type-I tilted Weyl semimetals is briefly presented.

Two-dimensional vibronic spectroscopy with semiclassical thermofield dynamics.

Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational-electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method.

Analyzing Cathode and Anode Spot Movements of Atmospheric Arc Plasma in Parallel Electrodes Using Thermal Field Theory and Thermal Nonequilibrium Model

It is necessary to elucidate the mechanism of atmospheric arc plasma movement and the variation in its physical properties for constructing an accurate virtual model while using digital twin technology to design a next‐generation direct current circuit breaker. In this study, the calculation setting for considering the thermal nonequilibrium effect on an electrode surface was established. Moreover, the thermal field theory was employed for simulating the cathode spot movement and a thermal nonequilibrium model was implemented for analyzing the triggering factor of the re‐strike phenomenon occurrence on the anode surface. It was found that heavy particles (ions and neutral particles) were transported forward by the cathode jet and not only caused an increment in the electrical conductivity on the anode surface, but also increased the electric field between the arc column and the anode surface. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Finite temperature applications in G\xf6del space-time

Temperature effects in a scalar field non-minimally coupled to gravity are investigated. The Thermo Field Dynamics formalism is used. This is a topological field theory that allows us to calculate different effects, such as the Stefan–Boltzmann law and the Casimir effect, on an equal footing. These phenomena are calculated assuming the Gödel space-time as a gravitational background. A possible implication of these results at the beginning of the universe is discussed.

Analogous Hawking Effect: S-Matrix and Thermofield Dynamics

We consider the full S-matrix in the scattering giving rise to analogous Hawking radiation in dispersive media. We show the general structure of the scattering in the weak dispersion approximation and discuss some unnoticed features of the primary process, with a possible generalization of the phenomenology of the Hawking effect. In particular, we stress that the Hawking particle and its antiparticle partner a priori could also be produced with different rates. We provide a general parameterization of the S-matrix, adopting the Iwasawa decomposition for the matrix itself. Then, we assume that a perturbative structure in a suitable sense is allowed and display the corresponding expansion. In connection with the general structure of the S-matrix at the leading order, we also consider the thermofield dynamics (TFD) framework and show that the TFD picture is still available, with a doubling of the degrees of freedom emerging in a natural way, as for the astrophysical black hole case. Furthermore, we show that particles on the thermal vacuum can be identified with real particles appearing in the scattering.

Variational Squeezed Davydov Ansatz for Realistic Chemical Systems with Nonlinear Vibronic Coupling.

Chemical systems normally possess strong nonlinear vibronic couplings at both zero and finite temperature. For the lowest-order quadratic couplings, here, we introduce a squeezing operator into a variational coherent-state-based method, Davydov ansatz, to simulate the quantum dynamics and the respective spectroscopy. Two molecular systems, pyrazine and the 2-pyridone dimer, are taken as calculated model systems, both of which involve nontrivial quadratic vibronic couplings in high- and low-frequency regions, respectively. Upon a comparison with the benchmarks, the method manifests its advantage for nonlinear couplings. The squeezed bases are also proven to be applicable for the finite temperature by adapting with the thermofield dynamics.

Running coupling constant in thermal ϕ4 theory up to two loop order

Using the imaginary time formalism in thermal field theory, we derive the running coupling constant and running mass in two loop order. In the process, we express the imaginary time formalism of Feynman diagrams as the summation of nonthermal quantum field theory (QFT) Feynman diagrams with coefficients that depend on temperature and mass. Renormalization constants for thermal ${\ensuremath{\phi}}^{4}$ theory were derived using simple diagrammatic analysis. Our model links the nonthermal QFT and the imaginary time formalism by assuming both have the same mass scale $\ensuremath{\mu}$ and coupling constant $g$. When these results are combined with the renormalization group equations and applied simultaneously to thermal and nonthermal proper vertex functions, the coupling constant and running mass with implicit temperature dependence are obtained. We evaluated pressure for scalar particles in two loop orders at the zero external momentum limit by substituting the running mass result in the quasiparticle model.

The methods of thermal field theory for degenerate quantum plasmas in astrophysical compact objects

In the study of degenerate plasmas contained within compact astrophysical objects, both special relativity and general relativity play important roles. After reviewing the existing treatment in the literature, here we employ the methods of relativistic thermal quantum field theory to compute the equation of states of degenerate matter for compact astrophysical objects such as the white dwarfs and the neutron stars. In particular, we compute the equation of states that include leading order corrections due to the finite temperature, the fine-structure constant as well as the effect of gravitational time dilation. We show that the fine-structure constant correction remains well-defined even in the non-relativistic regime in contrast to the existing treatment in the literature.

Analytical solution of surface tension of quark-hadron phase transition

By using the finite temperature field theory, the one-loop effective potential and the dynamics of the quantum chromodynamics deconfinement phase transition in the framework of Friedberg-Lee model are studied at finite temperature and density. Our results show that there is a first-order deconfinement phase transition for the full phase diagram, and the critical temperature is about 119.8 MeV for a zero chemical potential whereas the critical chemical is around 256.4 MeV when the temperature is fixed at <i>T</i> = 50 MeV. Moreover, in the thin-wall approximation, we investigate the dynamics of a strong first-order quark-hadron transition via homogeneous bubble nucleation in the Friedberg-Lee model. Under an appropriate boundary condition, the equation of motion for the <inline-formula><tex-math id="M3">\begin{document}$ \sigma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M3.png"/></alternatives></inline-formula> field is solved, then the evolutions of the bubble critical configuration with radius <inline-formula><tex-math id="M4">\begin{document}$ r $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M4.png"/></alternatives></inline-formula> at different temperatures and densities are calculated. The surface tension, the typical radius of the critical bubble and the shift in the coarse-grained free energy each as a function of temperature and chemical potential are obtained. In order to gain the reliability and advantages of the thin-wall approximation, our analytical results based on the thin-wall approximation are compared with those obtained by the exact numerical method accordingly. Finally, some consequences and possible applications of our results in the quark meson model and Polyakov quark meson model are also presented in the end of this paper.

Temperature effects for $$e^-+e^+\rightarrow \mu ^-+\mu ^+$$ scattering in very special relativity

The electron-positron scattering process is investigated in the context of very special relativity (VSR). This theory assumes that the true symmetry of nature is not the full Lorentz group, but some of its subgroups, such as the subgroups $SIM(2)$ and $HOM(2)$. In this context, the cross-section for electron-positron scattering at finite temperature is calculated. The effects of temperature are introduced using the Thermo Field Dynamics (TFD) formalism. Our result shows that the cross-section is changed due to both effects, the VSR contributions and temperature effects. An estimated value for the VSR parameter using experimental data available in the literature is discussed.

Non-Abelian electric field correlator at NLO for dark matter relic abundance and quarkonium transport

We perform a complete next-to-leading order calculation of the non-Abelian electric field correlator in a SU(Nc) plasma, which encodes properties of the plasma relevant for heavy particle bound state formation and dissociation, and is different from the correlator for the heavy quark diffusion coefficient. The calculation is carried out in the real-time formalism of thermal field theory and includes both vacuum and finite temperature contributions. By working in the Rξ gauge, we explicitly show the results are gauge independent, infrared and collinear safe. The renormalization group equation of this electric field correlator is determined by that of the strong coupling constant. Our next-to-leading order calculation can be directly applied to any dipole singlet-adjoint transition of heavy particle pairs. For example, it can be used to describe dissociation and (re)generation of heavy quarkonia inside the quark-gluon plasma well below the melting temperature, as well as heavy dark matter pairs (or charged co-annihilating partners) in the early universe.

TFD formalism: Applications to the scalar field in a Lorentz-violating theory

The Thermofield Dynamics (TFD) formalism is considered. In this context, a Lorentz-breaking scalar field theory is introduced. In contrast to the Matsubara formalism, the best-known approach to introducing the temperature effect, TFD is a real-time formalism and is a topological field theory. While in Matsubara the temperature effects are introduced as a consequence of a compactification of the field in a finite interval on the time axis, in the TFD this effect emerges through a condensed state related to the Bogoliubov transformation. An advantage of the TFD formalism is that different topologies, which lead to different effects, can be chosen. Here, three different topologies are considered. Then the Stefan-Boltzmann law and Casimir effect at zero and non-zero temperature are calculated. This is a unique feature of TFD, which allows us to treat different phenomena in the same way.