Temperature Dependence of Two- and Three-Gluon Condensates in the Instanton Vacuum

The two-gluon and three-gluon condensates at finite temperature are calculated in the framework of the grand partition function for a weak-interacting instanton medium of a disordered phase. The interference parts of both chromomagnetic and chromoelectric two-gluon condensates are found to be small but still significant for a quantitative determination of the value of the condensates at very low temperature, and negligible at the temperature above 1.5Λ_MS, with respect to their non-interference ones. The interference parts of the threegluon condensates are found to be quite small even at very low temperature. With the QCD scale parameter fixed by the value of the Lorentz invariant two-gluon condensate at zero temperature, the value of the three-gluon condensate at zero temperature is found to be coincident with the phenomenological estimate. The values of the gluon condensates decrease when temperature increases, and are negligible when the temperature goes beyond 2.5Λ_MS in the case of the SU_C(3) pure gauge theory.     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.     

Hadron resonance gas and nonperturbative QCD vacuum at finite temperature

Nonperturbative QCD vacuum with two light quarks at finite temperature was studied in a hadron resonance-gas model. Temperature dependences of the quark and gluon condensates in the confined phase were obtained. It is shown that the quark condensate and one-half (chromoelectric component) of the gluon condensate are evaporated at the same temperature corresponding to the quark-hadron phase transition. With allowance for the temperature shift of hadron masses, the critical temperature was found to be T _c ?190 MeV.     

In-Medium η′ Mass Reduction

In this talk, we present the reduction of the mass of η′-meson at finite temperature which leads to the enhancement of η′ contributions to the dilepton spectra from relativistic heavy ion collisions. QCD low energy theorem, together with the Witten–Veneziano formula, provides the relation of the η′ mass with gluon condensates.     

Mixed quark–gluon condensate at finite temperature and density in the global color symmetry model

We study the properties of mixed quark–gluon condensate at finite temperature and chemical potential in the framework of global color symmetry model. In comparing with the quark condensate, we confirm that both of these condensates give the same information about chiral phase transition. We also find that the ratio of these two condensates is insensitive to the temperature T and the chemical potential μ, which supports the conclusion obtained recently by the authors using quenched lattice QCD.     

Quarkonia at Finite T: An Approach Based On QCD Sum Rules and the Maximum Entropy Method

Quarkonium spectral functions at finite temperature are studied, making use of a recently developed method of analyzing QCD sum rules by the maximum entropy method. This approach enables us to directly obtain the spectral function from the sum rules, without having to introduce any specific assumption about its functional form. QCD sum rules for heavy quarkonia incorporate finite temperature effects in form of changing values of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which we extract from quenched lattice QCD calculations. As a result, it is found that the charmonium ground states of both S-wave and P-wave channels dissolve into the continuum already at temperatures around or slightly above the critical temperature T _c , while the bottomonium states are less influenced by temperature effects, surviving up to about 2.5 T _c or higher for S-wave and about 2.0 T _c for P-wave states.     

Thermal desorption of Ag from oxidized W

Thermal desorption spectra (TDS) of Ag condensates deposited at two substrate temperatures T_s = 300 K and T_s = 779 K have been obtained. A shift of the temperature T_m of the maximum of the desorption flux R_e was observed. It was established that the shift of the maximum depends on the value of the initial coverage σ₀. A significant difference was found to exist between TDS of silver condensates deposited on oxidized and clean W substrates due to differences in the mechanism of condensation. Silver condensates were deposited on oxidized W at different initial conditions (T_s, impingement rates R_i, etc.) but equal σ₀. The corresponding TDS were compared and a conclusion has been drawn that the shift of T_m is due to the different structure of Ag condensates. TDS of Ag condensates deposited at room temperature (T_s = 300 K) were interpreted using the method of Bauer et al. [J. Appl. Phys. 45 (1974) 5164: Surface Sci. 53 (1975) 87]. The dependence of the desorption flux R_e on the substrate temperature T_s and coverage σ was treated on the basis of the Polanyi-Wigner equation and some parameters of the condensation process were evaluated.     

Predicting spinor condensate dynamics from simple principles

We study the spin dynamics of quasi-one-dimensional F=1 condensates both at zero and finite temperatures for arbitrary initial spin configurations. The rich dynamical evolution exhibited by these nonlinear systems is explained by surprisingly simple principles: minimization of energy at zero temperature and maximization of entropy at high temperature. Our analytical results for the homogeneous case are corroborated by numerical simulations for confined condensates in a wide variety of initial conditions. These predictions compare qualitatively well with recent experimental observations and can, therefore, serve as a guidance for ongoing experiments.     

Stability of plane-wave Bose-Einstein condensation with spin-orbit coupling

In this paper, we prove analytically that the plane-wave Bose-Einstein condensates with spin-orbit coupling are stable in two dimensions at zero temperature. The SOC induced extra breaking of the O(2) symmetry of the ground state makes the goldstone modes more divergent in the infrared limit. But the depletions are still finite, which means the condensates are stable.     

On the problem of the existence of a supercooled liquid phase of cryovacuum ethanol condensates

Our previous IR-spectrometry and thermodesorption studies of thin films of cryovacuum ethanol condensates and comparison of these data with the results obtained in works of some groups have allowed us to make several conclusions relative to temperature ranges of existence of low-temperature states of ethanol. Newly acquired experimental data indicate that the cryovacuum condensates of ethanol formed at temperatures considerably below the glass transition temperature T _g ≈ 98 K pass through the state that can be characterized as a supercooled liquid phase in the course of subsequent thermally stimulated transformations. The temperature range of the solid-liquid transformation (97–100 K) agrees well with the data of researchers who studied the ethanol samples obtained by the vitrification from the liquid phase.     

QCD sum rules at finite temperature

Finite energy and Laplace transform QCD sum rules atT0 are analyzed, and predictions for vacuum condensates are compared with the low temperature expansion of the energy density and pressure. Results show a serious disagreement which indicates a breakdown of the FESR programme already at dimension four, and which invalidates Laplace transform sum rules, at least in their straightforward extension to finite temperature.     

Matter-wave vortices and solitons in anisotropic optical lattices

Using numerical methods, we construct families of vortical, quadrupole, and fundamental solitons in a two-dimensional (2D) nonlinear-Schrödinger/Gross-Pitaevskii equation which models Bose-Einstein condensates (BECs) or photonic crystals. The equation includes the attractive or repulsive cubic nonlinearity and an anisotropic periodic potential. Two types of anisotropy are considered, accounted for by the difference in the strengths of the 1D sublattices, or by a difference in their periods. The limit case of the quasi-1D optical lattice (OL), when one sublattice is missing, is included too. By means of systematic simulations, we identify stability limits for two species of vortex solitons and quadrupoles, of the rhombus and square types. In the attraction model, rhombic vortices and quadrupoles remain stable up to the limit case of the quasi-1D lattice. In the same model, finite stability limits are found for vortices and quadrupoles of the square type, in terms of the anisotropy parameter. In the repulsion model, rhombic vortices and quadrupoles are stable in large parts of the first finite bandgap (FBG). Another species of partly stable anisotropic states is found in the second FBG, subfundamental dipoles, each squeezed into a single cell of the OL. Square-shaped quadrupoles are completely unstable in the repulsion model, while vortices of the same type are stable only in weakly anisotropic OL potentials.     

Dyson-Schwinger approach to color superconductivity at finite temperature and density

We investigate the phases of dense QCD matter at finite temperature with Dyson-Schwinger equations for the quark propagator for N _f = 2 + 1 flavors. For the gluon propagator we take a fit to quenched lattice data and add quark-loop effects perturbatively in a hard-thermal-loop-hard-dense-loop approximation. We consider 2SC and CFL-like pairing with chiral up and down quarks and massive strange quarks and present results for the condensates and the phase diagram. We find a dominant CFL phase at chemical potentials larger than 500-600MeV. At lower values of the chemical potential we find a 2SC phase, which also exists in a small band at higher temperatures for larger chemical potentials. With values of 20–30 MeV, the critical temperatures to the normal phase turn out to be quite small.     

An efficient numerical method for computing dynamics of spin F = 2 Bose–Einstein condensates

In this paper, we extend the efficient time-splitting Fourier pseudospectral method to solve the generalized Gross–Pitaevskii (GP) equations, which model the dynamics of spin F = 2 Bose–Einstein condensates at extremely low temperature. Using the time-splitting technique, we split the generalized GP equations into one linear part and two nonlinear parts: the linear part is solved with the Fourier pseudospectral method; one of nonlinear parts is solved analytically while the other one is reformulated into a matrix formulation and solved by diagonalization. We show that the method keeps well the conservation laws related to generalized GP equations in 1D and 2D. We also show that the method is of second-order in time and spectrally accurate in space through a one-dimensional numerical test. We apply the method to investigate the dynamics of spin F = 2 Bose–Einstein condensates confined in a uniform/nonuniform magnetic field.     

Quark condensates in non-Abelian fields at finite temperature

The properties of quark condensates in static non-Abelian fields of the chromomagnetic types are investigated. The dependence of the condensate on the field strength and the temperature is discussed. It is shown that the principal term of the asymptotic expansion for all the investigated field types has the form v^–2 in the high-temperature limit. An expansion is obtained for the quantity in the limit of an arbitrary, uniform, weak field for T=0 and at finite temperature.M. V. Lomonosov State University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 39–52, January, 1994.     

Effect of Dzyaloshinskii−Moriya interactions on Kagome anti-ferromagnetic clusters

The low energy and low temperature behavior of a few finite size Kagome clusters, including mixed spin systems of S=1/2 and S=1, with the nearest neighbor Heisenberg antiferromagnetic model is studied under the influence of out-of-plane Dzyaloshinskii?Moriya interactions (DMI) within the exact diagonalization formalism. The ground state of all the finite size systems is found to be present in the lowest spin sector with a finite gap to the lowest magnetic excitation irrespective of the strength of out-of-plane DMI. The energy level structures within the non-magnetic ground state and the lowest magnetic state have been studied for all the systems as a function of DMI. The characteristic signature of such low-lying non-magnetic excitations is reflected in the low temperature behavior of the specific heat. It is also found that the ground state chiral structure (characterized by the vector chiral order of the system) in the xy-plane shows sharp changes as a function of out-of-plane DMI at level crossing or avoided crossing regions. The in-plane spin ordering for each system is also studied with the estimation of static structure factor as a response to the varying strength of DMI.     

Equation of state for pion-condensed neutron matter at finite temperature

The equation of state for neutron matter in the presence of a pion condensate is investigated at finite, but small temperature within the σ model. It is found that a transition of van der Waals type takes place at low temperature for sufficiently strong effective p-wave interaction, which disappears however beyond a critical temperature T_c. Within a wide variety of model assumptions, an upper limit of about 50 MeV is found for T_c.     

Low-energy theorems of hot and dense QCD in a magnetic field

The nonperturbative QCD vacuum at finite temperature and a finite baryon density in an external magnetic field is studied. Equations that relate nonperturbative condensates to the thermodynamic pressure for T ≠ 0, μ _q ≠ 0, and H ≠ 0 are obtained, and low-energy theorems are derived.     

Pion condensation of quark matter in a static Einstein universe

In the framework of an extended Nambu–Jona-Lasinio model we study pion condensation in quark matter with an asymmetric isospin composition. We treat this against the gravitational field of a static Einstein universe at finite temperature and chemical potential. This particular choice of the gravitational field configuration enables us to investigate phase transitions of the system with exact consideration of the role of this field in the formation of quark and pion condensates. Also, we point out its influence on the phase portraits. We demonstrate the effect of oscillations of the thermodynamic quantities as functions of the curvature and also refer to a certain similarity between the behavior of these quantities as functions of curvature and finite temperature. Finally, the role of quantum fluctuations for spontaneous symmetry breaking in the case of a finite volume of the universe is briefly discussed.