QCD at finite temperature—a variational approach

We develop here a nonperturbative framework to study quantum chromodynamics (QCD) at finite temperatures using the thermofield dynamics (TFD) method of Umezawa. The methodology considered here is selfconsistent and variational. There is a dynamical generation of a magnetic gluon mass. This eliminates the infrared problems associated with perturbative QCD calculations at finite temperatures. We obtain here the thermodynamical quantities like free energy density, pressure and entropy density. We also calculate the temperature dependence of SVZ parameter . The condensate vanishes at the critical temperature in accordance with recent hot sum rule calculations. The present method gives an insight to the vacuum structure in QCD at zero temperature as well as at finite temperatures in a coordinated manner.     

Čerenkov radiation at finite temperature

A power formula for erenkov radiation at finite temperature is derived in the framework of the generalized finite-temperature Cutkosky rules. Spins 1/2 and 0 are considered.     

“Phase transitions” at finite temperature in finite systems

Indications of phase transitions (present in the thermodynamic limit) are seen in the solution for a finite number of particles of an exactly solvable model. The gross structure of the implied exact “phase diagram” is reproduced by self-consistent mean-field approximations, but not, in general, the precise location of the “phase” boundaries.     

Bound fermion states in the field of a soliton of the nonlinear O(3) σ model

The (2 + 1)-dimensional nonlinear O(3) σ model whose n field is coupled to the fermion field by the Yukawa interaction has been examined. The cases of the isosinglet and isodoublet fermion fields with respect to the internal symmetry group have been considered. It has been shown that bound states of the fermion in the n field of a soliton of the nonlinear O(3) σ model exist for some variants of the Yukawa interaction. The absence of zeroth fermion modes in the n field of the soliton has been established. The properties of the ground state of the fermion have been numerically studied. In particular, it has been shown that an increase in the spatial size of the soliton results in a decrease in the energy of the ground state. This leads to the instability of the soliton in a certain region of the parameters of the model.     

Self-deflection of a bright soliton in a separate bright－dark spatial soliton pair based on a higher-order space charge field

The self-deflection of a bright solitary beam can be controlled by a dark solitary beam via a parametric coupling effect between the bright and dark solitary beams in a separate bright－dark spatial soliton pair supported by an unbiased series photorefractive crystal circuit. The spatial shift of the bright solitary beam centre as a function of the input intensity of the dark solitary beam (\hatρ) is investigated by taking into account the higher-order space charge field in the dynamics of the bright solitary beam via both numerical and perturbation methods under steady-state conditions. The deflection amount (Δs_0), defined as the value of the spatial shift at the output surface of the crystal, is a monotonic and nonlinear function of \hatρ. When \hatρ is weak or strong enough, Δs_0 is, in fact, unchanged with \hatρ, whereas Δs_0 increases or decreases monotonically with \hatρ in a middle range of \hatρ. The corresponding variation range (δs) depends strongly on the value of the input intensity of the bright solitary beam (r). There are some peak and valley values in the curve of δs versus r under some conditions. When \hatρ increases, the bright solitary beam can scan toward both the direction same as and opposite to the crystal's c-axis. Whether the direction is the same as or opposite to the c-axis depends on the parameter values and configuration of the crystal circuit, as well as the value of r. Some potential applications are discussed.     

Self-deflection of bright soliton in a separate bright-dark screening soliton pair based on higher-order space charge field

Based on the interaction of the separate soliton pair, the self-deflection of the bright screening soliton in a bright-dark pair is studied by taking the higher order space charge field into account. Both numerical and analytical methods are adopted to obtain the result that the higher order of space charge field can enhance the deflection process of the bright soliton and varying the peak intensity of the dark soliton can influence the self-deflection strongly. The expression of the deflection distance with the dark soliton's peak intensity is derived, and some corresponding properties of the self-deflection process are figured out.     

Analytic structure of ρ meson propagator at finite temperature

We analyse the structure of one-loop self-energy graphs for the ρ meson in real time formulation of finite temperature field theory. We find the discontinuities of these graphs across the unitary and the Landau cuts. These contributions are identified with different sources of medium modification discussed in the literature. We also calculate numerically the imaginary and the real parts of the self-energies and construct the spectral function of the ρ meson, which are compared with an earlier determination. A significant contribution arises from the unitary cut of the π ω loop, that was ignored so far in the literature.     

Gaussian effective potential for theФ 4-theory in two dimensions at finite temperature

The Gaussian effective potential for the ground state of the ⁴-theory in 1+1 dimensions shows a symmetry breaking above a critical coupling constant. The restoration of the symmetry at high temperatures and the role of the renormalization are discussed.     

Real-time propagators at finite temperature and chemical potential

We derive a form of spectral representations for all bosonic and fermionic propagators in the real-time formulation of field theory at finite temperature and chemical potential. Besides being simple and symmetrical between the bosonic and the fermionic types, these representations depend explicitly on analytic functions only. This property allows for a simple evaluation of loop integrals in the energy variables over propagators in this form, even in the presence of chemical potentials, which is not possible for their conventional form.     

Maxwell–Chern–Simons Casimir effect at finite temperature

We will apply the Feynman path integral method to discuss the Casimir force of Maxwell–Chern–Simons gauge field at finite temperature between two parallel ideal conducting wires.     

Instability of a two-dimensional Bose–Einstein condensate with Rashba spin–orbit coupling at finite temperature

We prove that in a two-dimensional homogeneous boson system with Rashba spin–orbit coupling, Bose–Einstein condensate with plane-wave order is unstable at finite temperature. The calculations are based on a nonlinear sigma model scheme. The density wave contributions to the thermal deletions are divergent in the infrared limit. The behavior of the divergence is different from that without spin–orbit coupling.     

Ultradilute self-bound quantum droplets in Bose–Bose mixtures at finite temperature

We theoretically investigate the finite-temperature structure and collective excitations of a self-bound ultradilute Bose droplet in a flat space realized in a binary Bose mixture with attractive inter-species interactions on the verge of meanfield collapse. As the droplet formation relies critically on the repulsive force provided by Lee–Huang–Yang quantum fluctuations, which can be easily compensated by thermal fluctuations, we find a significant temperature effect in the density distribution and collective excitation spectrum of the Bose droplet. A finite-temperature phase diagram as a function of the number of particles is determined. We show that the critical number of particles at the droplet-to-gas transition increases dramatically with increasing temperature. Towards the bulk threshold temperature for thermally destabilizing an infinitely large droplet, we find that the excitation-forbidden, self-evaporation region in the excitation spectrum, predicted earlier by Petrov using a zero-temperature theory, shrinks and eventually disappears. All the collective excitations, including both surface modes and compressional bulk modes, become softened at the droplet-to-gas transition. The predicted temperature effects of a self-bound Bose droplet in this work could be difficult to measure experimentally due to the lack of efficient thermometry at low temperatures. However, these effects may already present in the current cold-atom experiments.     

The λφ4 coupling at high temperature

Some erroneous claims about λφ⁴ scalar field theory are corrected. In particular, the coupling λ(T) is shown to grow logarithmically with temperature for large T.     

Massive Yang–Mills for vector and axial-vector spectral functions at finite temperature

The hadronic mechanism which leads to chiral symmetry restoration is explored in the context of the ρπa₁$\rho \pi a_1$ system using Massive Yang–Mills, a hadronic effective theory which governs their microscopic interactions. In this approach, vector and axial-vector mesons are implemented as gauge bosons of a local chiral gauge group. We have previously shown that this model can describe the experimentally measured vector and axial-vector spectral functions in vacuum. Here, we carry the analysis to finite temperatures by evaluating medium effects in a pion gas and calculating thermal spectral functions. We find that the spectral peaks in both channels broaden along with a noticeable downward mass shift in the a₁$a_1$ spectral peak and negligible movement of the ρ$\rho$ peak. The approach toward spectral function degeneracy is accompanied by a reduction of chiral order parameters, i.e., the pion decay constant and scalar condensate. Our findings suggest a mechanism where the chiral mass splitting induced in vacuum is burned off. We explore this mechanism and identify future investigations which can further test it.     

Transport properties of the two-dimensional electron gas in AlP quantum wells at finite temperature including magnetic field and exchange–correlation effects

We investigate the transport scattering time, the single-particle relaxation time and the magnetoresistance of a quasi-two-dimensional electron gas in a GaP/AlP/GaP quantum well at zero and finite temperatures. We consider the interface-roughness and impurity scattering, and study the dependence of the mobility, scattering time and magnetoresistance on the carrier density, temperature and local-field correction. In the case of zero temperature and Hubbard local-field correction our results reduce to those of Gold and Marty (Physica E 40 (2008) 2028; Phys. Rev. B 76 (2007) 165309). We also discuss the possibility of a metal–insulator transition which might happen at low density.     

On colour non-singlet representations of the quark–gluon system at finite temperature

We use a group theoretical technique to project out the partition function for a system of quarks, antiquarks and gluons onto a particular representation of the internal symmetry group SU(3): the colour singlet, colour octet and colour 27-plet, at finite temperature. We do this to calculate the thermodynamic quantities for those representations. We also calculate the change in free energy of the plasma droplet formed from the hot hadronic gas. We find that the size of the droplet in the colour-octet representation is smaller than that in the colour-singlet representations at different temperatures in the vicinity of the critical temperatures of the phase transitions. Received: 1 February 1999 / Revised version: 24 February 2000 / Published online: 18 May 2000     

Thermal vacuum state for the two-coupled-oscillator model at finite temperature： Derivation and application

Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state （TVS） for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann-Feynman theorem and the entroy variation in the context of the TVS.