High-temperature Approximation Research Articles

Electroweak phase transition with a double well done doubly well

We revisit the electroweak phase transition in the scalar singlet extension of the standard model with a ℤ2 symmetry. In significant parts of the parameter space the phase transition occurs in two steps — including canonical benchmarks used in experimental projections for gravitational waves. Domain walls produced in the first step of the transition seed the final step to the electroweak vacuum, an effect which is typically neglected but leads to an exponentially enhanced tunnelling rate. We improve previous results obtained for the seeded transition, which made use of the thin-wall or high temperature approximations, by using the mountain pass algorithm that was recently proposed as a useful tool for seeded processes. We then determine the predictions of the seeded transition for the latent heat, bubble size and characteristic time scale of the transition. Differences compared to homogeneous transitions are most pronounced when there are relatively few domain walls per hubble patch, potentially leading to an enhanced gravitational wave signal. We also provide a derivation of the percolation criteria for a generic seeded transition, which applies to the domain wall seeds we consider as well as to strings and monopoles.

Gravitational waves and tadpole resummation: Efficient and easy convergence of finite temperature QFT

We demonstrate analytically and numerically that “optimized partial dressing” (OPD) thermal mass resummation, which uses gap equation solutions inserted into the tadpole, efficiently tames finite-temperature perturbation theory calculations of the effective thermal potential, without necessitating use of the high-temperature approximation. An analytical estimate of the scale dependence for OPD resummation, standard Parwani resummation (Daisy resummation), and dimensional reduction shows that OPD has similar scale dependence to dimensional reduction, greatly improving Parwani resummation. We also elucidate how to construct and solve the gap equation for realistic numerical calculations, and demonstrate OPD’s improved accuracy for a toy scalar model. OPD’s improved accuracy is most physically significant when the high-temperature approximation breaks down, rendering dimensional reduction unusable and Parwani resummation highly inaccurate, with the latter underestimating the maximal gravitational wave amplitude for the model by 2 orders of magnitude compared to OPD. Our work highlights the need to bring theoretical uncertainties under control even when analyzing broad features of a model. Given the simplicity of the OPD compared to two-loop dimensional reduction, as well as the ease with which this scheme handles departures from the high-temperature expansion, we argue this scheme has great potential in analyzing the parameter space of realistic beyond the Standard Model models. Published by the American Physical Society 2024

High-temperature modifications of charged Casimir wormholes

In this work, we extend the investigation of the consequences of thermal fluctuations on the Casimir effect within the context of a traversable wormhole, recently proposed by Garattini & Faizal, arXiv:2403.15174 [gr-qc], subject to charge contributions. Specifically, we focus on scenarios where the plates exhibit both constant and radial variations. In our analysis, we initially concentrate on the high temperature approximation, considering solely the influence of charge on the thermal Casimir wormholes. Additionally, upon incorporating Generalized Uncertainty Principle (GUP) corrections to the Casimir energy, we obtain a new class of wormhole solutions. Notably, we establish that the flare-out condition remains consistently satisfied. Intriguingly, our findings reveal that both the charge and GUP contributions serve to further enlarge the throat's size in the radial variation.

A Computational Study of the Electronic Energy and Charge Transfer Rates and Pathways in the Tetraphenyldibenzoperiflanthene/Fullerene Interfacial Dyad.

The electronic transition rates and pathways underlying interfacial charge separation in tetraphenyldibenzoperiflanthene:fullerene (DBP:C70) blends are investigated computationally. The analysis is based on a polarization-consistent framework employing screened range-separated hybrid functional in a polarizable continuum model to parametrize Fermi's golden rule rate theory. The model considers the possible transitions within the 25 lowest excited states of a DBP:C70 dyad that are accessible by photoexcitation. The different identified pathways contributing to charge carrier generation include electron and hole transfer and backtransfer, exciton transfer, and internal relaxation steps. The larger density of states of C70 appears to explain the previously observed larger efficiency for charge separation through hole transfer mechanism. We also analyze the validity of the high-temperature and short-time semiclassical approximations of the FGR theory, where both overestimated and underestimated Marcus theory based constants can be affected.

Zero-cost corrections to influence functional coefficients from bath response functions.

Recent work has shown that it is possible to circumvent the calculation of the spectral density and directly generate the coefficients of the discretized influence functionals using data from classical trajectory simulations. However, the accuracy of this procedure depends on the validity of the high temperature approximation. In this work, an alternative derivation based on the Kubo formalism is provided. This enables the calculation of additional correction terms that increases the range of applicability of the procedure to lower temperatures. Because it is based on the Kubo-transformed correlation function, this approach allows the direct use of correlation functions obtained from methods such as ring-polymer molecular dynamics and centroid molecular dynamics in determining the influence functional coefficients for subsequent system-solvent simulations. The accuracy of the original procedure and the corrected procedure is investigated across a range of parameters. It is interesting that the correction term comes at zero additional cost. Furthermore, it is possible to improve upon the correction using zero-cost physical intuition and heuristics making the method even more accurate.

Hamiltonian of mean force in the weak-coupling and high-temperature approximations and refined quantum master equations

The Hamiltonian of mean force is a widely used concept to describe the modification of the usual canonical Gibbs state for a quantum system whose coupling strength with the thermal bath is non-negligible. Here, we perturbatively derive general approximate expressions for the Hamiltonians of mean force in the weak-coupling approximation and in the high-temperature one. We numerically analyze the accuracy of the corresponding expressions and show that the precision of the Bloch–Redfield equantum master equation can be improved if we replace the original system Hamiltonian by the Hamiltonian of mean force.

Thermodynamics of the independent harmonic oscillators with different frequencies in the Tsallis statistics in the high physical temperature approximation

We study the thermodynamic quantities in the system of the $N$ independent harmonic oscillators with different frequencies in the Tsallis statistics of the entropic parameter $q$ ($1<q<2$) with escort average. The self-consistent equation is derived, and the physical quantities are calculated with the physical temperature. It is found that the number of oscillators is restricted below $1/(q-1)$. The energy, the R\'enyi entropy, and the Tsallis entropy are obtained by solving the self-consistent equation approximately at high physical temperature and/or for small deviation $q-1$. The energy is $q$-independent at high physical temperature when the physical temperature is adopted, and the energy is proportional to the number of oscillators and physical temperature at high physical temperature. The form of the R\'enyi entropy is similar to that of von-Neumann entropy, and the Tsallis entropy is given through the R\'enyi entropy. The physical temperature dependence of the Tsallis entropy is different from that of R\'enyi entropy. The Tsallis entropy is bounded from the above, while the R\'enyi entropy increases with the physical temperature. The ratio of the Tsallis entropy to the R\'enyi entropy is small at high physical temperature.

Multiscale Study of the Charge Transport Properties of Silicone Rubber Oligomers.

Polymer dielectrics are widely used as insulation in electronic and electrical equipment. The charge transport process in polymer dielectrics under a high electric field, which is considered to result in electrical aging and even breakdown of equipment insulation, has attracted considerable attention. Based on a localized charge transfer model, the charge transport mechanism for typical silicone rubber (SR) insulating materials was studied by multiscale methods. A model of silicone rubber oligomers under standard conditions was generated by classical molecular dynamics. The frontier molecular orbitals and projected density of states for the SR oligomer were obtained via quantum chemistry methods. The electronic coupling, reorganization energy, and free energy difference for both electron and hole transfer processes between adjacent SR molecules in the molecular dynamics model were calculated. Both hole transfer and electron transfer in SR conform to an intermolecular hopping mechanism due to their high intramolecular reorganization energy and low intermolecular electronic coupling. The results of normal mode analysis for reorganization energy indicate that the high-temperature approximation holds for charge transport in SR around or above room temperature. The charge transfer trajectory and charge mobility in SR were simulated based on kinetic Monte Carlo simulations. The hole and electron mobilities at room temperature were calculated to be 7.24 × 10-11 and 2.76 × 10-9 cm2/Vs, respectively, which agrees with the experimental data. Both electron transport and hole transport in SR show thermal activation characteristics, with corresponding activation energies of 358 and 314 meV, respectively. This work suggests a physical model to describe the charge transport process in SR polymer dielectrics.

A low-temperature quantum Fokker-Planck equation that improves the numerical stability of the hierarchical equations of motion for the Brownian oscillator spectral density.

We investigate the numerical stability of the hierarchical equations of motion (HEOM) method applied to systems with the Brownian oscillator (BO) and multimode BO (MBO) spectral densities. It is shown that, with the increase in the system-bath coupling strength, the standard HEOM may become unstable, and a simple increase in the truncation depth of the HEOM cannot remove the instability at long times. To solve this problem, we first show that the high-temperature approximation of the HEOM with the BO spectral density is equivalent to the celebrated quantum Fokker-Planck equation (QFPE). By starting from the HEOM, we then derive a new multidimensional phase space differential equation that generalizes the QFPE to arbitrary temperature. It is further shown that the numerical instability can be removed if the new low-temperature QFPE is expanded in a basis set different than the one that leads to the conventional HEOM. The matrix product state method is also employed to propagate the new equation based on the low-temperature QFPE and to resolve the numerical instability problem for an electron transfer model with the MBO spectral density presented in the recent literature.

Mixed quantum classical reaction rates based on the phase space formulation of the hierarchical equations of motion

In a previous work [J. Chem. Phys. 140, 174105 (2014)], we have shown that a mixed quantum classical (MQC) rate theory can be derived to investigate the quantum tunneling effects in the proton transfer reactions. However, the method is based on the high temperature approximation of the hierarchical equation of motion (HEOM) with the Debye-Drude spectral density, and results in a multistate Zusman type of equation. We now extend this theory to include quantum effects of the bath degrees of freedom. By writing the full HEOM into a multidimensional partial differential equation in phase space, we can define a new reaction coordinate, and the previous method can be generalized to the full quantum regime. The validity of the new method is demonstrated by using numerical examples, including the spin-Boson model, and the double well model for proton transfer reaction. The new method is found to resolve some key problems of the previous theory based on high temperature approximation, including possible numerical instability in long time simulation and wrong rate constant at low temperatures.

Vacuum structure and electroweak phase transition in singlet scalar dark matter

In the presence of a real singlet scalar field with Z2 symmetry in addition to the Higgs field in the Standard Model, we analytically investigate all possible one-step and two-step electroweak phase transitions (EWPT) in the high-temperature expansion limit. In particular, we examine the possibility of a first-order phase transition in an intermediate temperature interval of the universe for two-step scenarios. In all scenarios, we provide with necessary conditions on the parameters of the model to address a first- or second-order phase transition if ever possible in the high-temperature approximation. We show that among all possible EWPT channels in this model, only the two-step phase transition (0,0)→(0,w)→(v,0) can be of first-order type, either in the first or second step. The conditions obtained for EWPT is confronted with the dark matter (DM) and collider constraints. It is shown that the second-order one-step (0,0)→(v,0) scenario can evade the DM constraints, but it is not accessible to future colliders. The two-step first-order EWPT scenario (0,0)→(0,w)→(v,0), except for small DM masses, is excluded by direct detection experiments XENON1T/LUX, but it is accessible in future colliders ILC/TLEP.

Singlet-assisted electroweak phase transition at two loops

We investigate the electroweak phase transition in the real-singlet extension of the Standard Model at two-loop level, building upon existing one-loop studies. We calculate the effective potential in the high-temperature approximation and detail the required resummations at two-loop order. In typical strong-transition scenarios, we find deviations of order $20\% - 50\%$ from one-loop results in transition strength and critical temperature for both one- and two-step phase transitions. For extremely strong transitions, the discrepancy with one-loop predictions is even larger, presumably due to sizable scalar couplings in the tree-level potential. Along the way, we obtain a dimensionally-reduced effective theory applicable for non-perturbative lattice studies of the model.

Padé approximant approach to singular properties of quantum gases: the ideal cases

In this paper, we show how to recover the low-temperature and high-density information of ideal quantum gases from the high-temperature and low-density approximation by the Padé approximant. The virial expansion is a high-temperature and low-density expansion and in practice, often, only the first several virial coefficients can be obtained. For Bose gases, we determine the BEC phase transition from a truncated virial expansion. For Fermi gases, we recover the low-temperature and high-density result from the virial expansion.

Temperature-Frequency Controlling the Characteristics of a Pulsating Brownian Ratchet with Slightly Fluctuating Potential Energy

Within the approximation of slight fluctuations of the nanoparticle potential energy, we developed a method for calculating the characteristics of a Brownian ratchet (a complex nonlinear system capable of extracting useful work from unbiased nonequilibrium fluctuations). The method is suitable for studying the mechanisms and modes of functioning of artificial nanomotors. Unlike the effort-consuming obtaining and applying for this studying the Green's functions of the coordinate representation which describe diffusion in the stationary component of the potential, the proposed method operates with the Fourier representation of both the control and desired functions. That allows calculating the Green's functions as inverse matrices in the space of Fourier harmonics and finding the average velocity of a Brownian ratchet with an arbitrary spatial and temporal dependence of the potential energy. To illustrate the method, an analysis has been performed of the functioning of a ratchet in which the directional motion of nanoparticles arises due to small stochastic fluctuations of an asymmetric sawtooth potential profile with an arbitrary barrier-heightto- thermal-energy ratio. It is shown that, with a harmonic coordinate dependence of these fluctuations, a change in the direction and intensity of the ratchet effect is controlled not only by tuning the magnitude of their phase shift relative to the sawtooth potential (the fact revealed before in the high-temperature approximation), but also by changing the temperature and the frequency of fluctuations. The nontrivial dependencies of the ratchet velocity on the geometric, frequency, and energy parameters of the system are obtained by numerical implementing the proposed calculation method.

Spin relaxation in Cs2CuCl4−xBrx

The quantum-spin $S=1/2$ chain system ${\mathrm{Cs}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{4}$ is of high interest due to competing antiferromagnetic intrachain $J$ and interchain exchange ${J}^{\ensuremath{'}}$ interactions and represents a paramount example for Bose-Einstein condensation of magnons [R. Coldea et al., Phys. Rev. Lett. 88, 137203 (2002)]. Substitution of chlorine by bromine allows tuning the competing exchange interactions and corresponding magnetic frustration. Thereby, anisotropic exchange contributions may be decisive for the resulting ground state. Here we report on electron spin resonance (ESR) in single crystals of ${\mathrm{Cs}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{4\ensuremath{-}x}{\mathrm{Br}}_{x}$ with the aim to analyze the evolution of these anisotropic exchange contributions. The main source of the ESR linewidth is attributed to the uniform Dzyaloshinskii-Moriya interaction. The vector components of the Dzyaloshinskii-Moriya interaction are determined from the angular dependence of the ESR spectra using a high-temperature approximation. The obtained results support the site selectivity of the Br substitution suggested from the evolution of lattice parameters and magnetic susceptibility dependent on the Br concentration.

Weyl–Wigner representation of canonical equilibrium states

The Weyl–Wigner representations for canonical thermal equilibrium quantum states are obtained for the whole class of quadratic Hamiltonians through a Wick rotation of the Weyl–Wigner symbols of Heisenberg and metaplectic operators. The behavior of classical structures inherently associated to these unitaries is described under the Wick mapping, unveiling that a thermal equilibrium state is fully determined by a complex symplectic matrix, which sets all of its thermodynamical properties. The four categories of Hamiltonian dynamics (parabolic, elliptic, hyperbolic and loxodromic) are analyzed. Semiclassical and high temperature approximations are derived and compared to the classical and/or quadratic behavior.

Spin Thermometry: A Straightforward Measure of Millikelvin Deuterium Spin Temperatures Achieved by Dynamic Nuclear Polarization.

Dynamic nuclear polarization of samples at low temperatures, typically between 1.2 and 4.2 K, allows one to achieve spin temperatures of as low as 2 mK so that for many nuclear isotopes the high-temperature approximation is violated for the nuclear Zeeman interaction. This leads to characteristic asymmetries in powder spectra. We show that the line shapes due to the quadrupolar couplings of deuterium spins present in virtually all solvents used for such experiments (DNP juice) allow the quick yet accurate determination of the deuterium spin temperature or, equivalently, the deuterium polarization. The observation of quadrupolar echoes excited by small flip-angle pulses allows one to monitor the build-up and decay of the positive or negative deuterium polarization.

Magnetization dynamics of the material with spin triplet states under the action of a weak varying field and spin-lattice interaction in zero constant field

The anisotropic dynamics of spin triplet states (STS) of molecular single crystals in zero constant and weak varying magnetic fields (weakness means the absence of saturation at the steady state and of the nutation at the pulse EPR) directed along the molecular axes, is analytically investigated. The equations are derived for the free motion of the sample magnetization, describing its linear oscillations along that molecular axis, along which its nonzero initial value was created. The tensor of the steady-state dynamical susceptibility to the varying field is found. The result of the action of a short MW pulse on STS is analytically described, containing a periodic dependence on the pulse duration and its detuning. Abovementioned results can be applied also to I=1 NMR, what is important for nitrogen-containing explosives and narcotics monitoring. The anisotropic dynamics of electron spin-lattice relaxation (SLR) at its one-phonon mechanism is investigated without the high temperature approximation over the phonon temperature; the SLR rates of the separate transitions of STS are calculated; the corresponding SLR probabilities are written in the form, which supposes the fractal dimensionality d of a lattice; the results with d=4/3 agree well with the experimental data in STS of the buried tryptophan of ribonuclease T1.

Photon dispersion relations in A0-background

We calculate the photon dispersion relations generated by the quark loop in a quark-gluon plasma with the color A0-background condensate \( A_0^c = A_0^{c3} + A_0^{c8} = {\rm const}\) . It is found that both transversal and longitudinal modes are exited. They have a gap at low momenta and are stable in the high-temperature approximation. The background fields act as imaginary chemical potentials and decrease the photon frequencies compared to the case of zero background. This has phenomenological consequences, in particular, for direct photons radiated from plasma. Comparisons with the QED plasma with a chemical potential are discussed.

In Russian

Stochastic non-equilibrium processes can serve as a driving force for a Brownian motor. In this case, the simplest description of an induced directional motion is carried out under the approximation of small changes in potential energy of a particle compared to the thermal energy (the high-temperature or low-energy approximation). Within this approximation, characteristics of the stochastic process are included into the final analytical expressions for the average velocity of a Brownian motor only through lower correlation functions. The purpose of this article is to obtain these correlation functions for Markov stochastic processes of a general form. The Pauli master equation has been considered, which describes the kinetics of an N states system in terms of given transition rate constants. The general solution of this equation, expressed in terms of the eigenvalues and eigenfunctions of the transition rate matrix, has been specified for the cases of dichotomous fluctuations (N = 2) and fluctuations of transitions from the ground state into two symmetric excited ones (N = 3). To study the influence of a type of a correlation function on the average velocity of a Brownian motor, a spatially harmonic controlled signal is considered, with which the average motor velocity is proportional to the second-order correlation function. The introduction of the additional state allowed us to obtain a bell-shaped frequency dependence of the average motor velocity, with the maximum and the width of the bell easily controllable by the transition rate constants and with the diffusion coefficient which depends on temperature, a particle size, and medium viscosity. Dichotomous process, which is a particular case of the model considered, is characterized by the highest values of the average velocity. A three-level model is preferable in case of a narrower width of the bell-shaped frequency dependence is required.