Zero Temperature Case Research Articles

Quantum number projection at finite temperature via thermofield dynamics

Applying the thermo field dynamics, we reformulate exact quantum number projection in the finite-temperature Hartree-Fock-Bogoliubov theory. Explicit formulae are derived for the simultaneous projection of particle number and angular momentum, in parallel to the zero-temperature case. We also propose a practical method for the variation-after-projection calculation, by approximating entropy without conflict with the Peierls inequality. The quantum number projection in the finite-temperature mean-field theory will be useful to study effects of quantum fluctuations associated with the conservation laws on thermal properties of nuclei.

Non-Markovian qubit dynamics in a thermal field bath: Relaxation, decoherence, and entanglement

We study the non-Markovian dynamics of a qubit made up of a two-level atom interacting with an electromagnetic field (EMF) initially at finite temperature. Unlike most earlier studies where the bath is assumed to be fixed, we study the coherent evolution of the combined qubit-EMF system, thus allowing for the back-action from the bath on the qubit and the qubit on the bath in a self-consistent manner. In this way we can see the development of quantum correlations and entanglement between the system and its environment, and how that affects the decoherence and relaxation of the system. We find non-exponential decay for both the diagonal and non-diagonal matrix elements of the qubit's reduced density matrix in the pointer basis. From the diagonal elements we see the qubit relaxes to thermal equilibrium with the bath. From the non-diagonal elements, we see the decoherence rate beginning at the usually predicted thermal rate, but changing to the zero temperature decoherence rate as the qubit and bath become entangled. These two rates are comparable, as was shown before in the zero temperature case [C. Anastopoulos and B. L. Hu, Phys. Rev. A {\bf 62} (2000) 033821]. On the entanglement of a qubit with the EMF under this type of resonant coupling we calculated, for the qubit reduced density matrix, the fidelity and the von Neumann entropy, which is a measure of the purity of the density matrix. The present more accurate non-Markovian calculations predict lower loss of fidelity and purity as compared with the Markovian results. Generally speaking, with the inclusion of quantum correlations between the qubit and its environment, the non-Markovian processes tend to slow down the drive of the system to equilibrium, prolonging the decoherence and better preserving the fidelity and purity of the system.

Hot nuclear matter equation of state with a three-body force

The finite temperature Brueckner-Hartree-Fock approach is extended by introducing a microscopic three-body force. In the framework of the extended model, the equation of state of hot asymmetric nuclear matter and its isospin dependence have been investigated. The critical temperature of liquid-gas phase transition for symmetric nuclear matter has been calculated and compared with other predictions. It turns out that the three-body force gives a repulsive contribution to the equation of state which is stronger at higher density and as a consequence reduces the critical temperature of liquid-gas phase transition. The calculated energy per nucleon of hot asymmetric nuclear matter is shown to satisfy a simple quadratic dependence on asymmetric parameter $\ensuremath{\beta}$ as in the zero-temperature case. The symmetry energy and its density dependence have been obtained and discussed. Our results show that the three-body force affects strongly the high-density behavior of the symmetry energy and makes the symmetry energy more sensitive to the variation of temperature. The temperature dependence and the isospin dependence of other physical quantities, such as the proton and neutron single particle potentials and effective masses, are also studied. Due to the additional repulsion produced by the three-body force contribution, the proton and neutron single particle potentials are correspondingly enhanced as similar to the zero-temperature case.

Effects of an extraU(1)axial condensate on the radiative decayη′→γγat finite temperature

Supported by recent lattice results, we consider a scenario in which a U(1)-breaking condensate survives across the chiral transition in QCD. This scenario has important consequences on the pseudoscalar-meson sector, which can be studied using an effective Lagrangian model. In particular, generalizing the results obtained in a previous paper (where the zero-temperature case was considered), we study the effects of this U(1) chiral condensate on the radiative decay eta' --> gamma gamma at finite temperature.

Finite-Temperature Equation of State with Three-Body ForceCorrelations

The equation of state of asymmetric nuclear matter atfinite temperature is studied in the framework of theBrueckner–Hartree–Fock approximation which is extended to includethree-body force correlations. Due to the additional repulsion producedby three-body force contribution, the proton or neutron potentialenergy and effective mass are correspondingly enhanced. The symmetryenergy gradually becomes more sensitive to the temperature with theincreasing density compared with the result that only includes the twohole-line contribution. The asymmetry parameter dependence of symmetryenergy is also indicated. It is shown that there is the same linearrelation between symmetry energy and β2 as the zerotemperature case with β being the asymmetry parameter.

The Percolation Transition in the Zero-Temperature Domany Model

We analyze a deterministic cellular automaton $\sigma^{\cdot} = (\sigma^n : n \geq 0)$ corresponding to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice $\mathbb H$. The state space ${\cal S}_{\mathbb H} = \{-1, +1 \}^{\mathbb H}$ consists of assignments of -1 or +1 to each site of $\mathbb H$ and the initial state $\sigma^0 = \{\sigma_x^0 \}_{x \in {\mathbb H}}$ is chosen randomly with $P(\sigma_x^0 = +1) = p \in [0,1]$. The sites of $\mathbb H$ are partitioned in two sets $\cal A$ and $\cal B$ so that all the neighbors of a site x in $\cal A$ belong to $\cal B$ and vice versa, and the discrete time dynamics is such that the $\sigma^{\cdot}_x$'s with $x \in {\cal A}$ (respectively, $\cal B$) are updated simultaneously at odd (resp., even) times, making $\sigma^{\cdot}_x$ agree with the majority of its three neighbors. In [1] it was proved that there is a percolation transition at p=1/2 in the percolation models defined by $\sigma^n$, for all times $n \in [1, \infty]$. In this paper, we study the nature of that transition and prove that the critical exponents $\beta$, $\nu$ and $\eta$ of the dependent percolation models defined by $\sigma^n, n \in [1, \infty]$, have the same values as for standard two-dimensional independent site percolation (on the triangular lattice).

Heavy quark free energies and screening in SU(2) gauge theory

We study the properties of the free energy of infinitely heavy quark anti-quark pair in SU(2) gauge theory. By means of lattice Monte Carlo simulations we calculated the free energies in the singlet, triplet and color averaged channels, both in the confinement and in the deconfinement phase. The singlet and triplet free energies are defined in Coulomb gauge which is equivalent to their gauge invariant definitions recently introduced by Philipsen. We analyzed the short and the long distance behavior, making comparisons with the zero temperature case. The temperature dependence of the electric screening mass is carefully investigated. The order of the deconfining transition is manifest in the results near T_c and it allows a reliable test of a recently proposed method to renormalize the Polyakov loop.

Cardy’s formula for some dependent percolation models

We prove Cardy’s formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany’s stochastic Ising ferromagnet on the hexagonal lattice ℍ(with alternating updates of two sublattices) [7]; it may also be realized on the triangular lattice T with flips when a site disagrees with six, five and sometimes four of its six neighbors.

Freezing in Ising ferromagnets.

We investigate the final state of zero-temperature Ising ferromagnets that are endowed with single-spin-flip Glauber dynamics. Surprisingly, the ground state is generally not reached for zero initial magnetization. In two dimensions, the system reaches either a frozen stripe state with probability approximately 1/3 or the ground state with probability approximately 2/3. In greater than two dimensions, the probability of reaching the ground state or a frozen state rapidly vanishes as the system size increases; instead the system wanders forever in an isoenergy set of metastable states. An external magnetic field changes the situation drastically-in two dimensions the favorable ground state is always reached, while in three dimensions the field must exceed a threshold value to reach the ground state. For small but nonzero temperature, relaxation to the final state proceeds first by formation of very long-lived metastable states, as in the zero-temperature case, before equilibrium is reached.

Hysteretic dynamics of domain walls at finite temperatures.

Theory of domain wall motion in a random medium is extended to the case when the driving field is below the zero-temperature depinning threshold and the creep of the domain wall is induced by thermal fluctuations. Subject to an ac drive, the domain wall starts to move when the driving force exceeds an effective threshold which is temperature and frequency dependent. Similar to the case of zero temperature, the hysteresis loop displays three dynamical phase transitions at increasing ac field amplitude h(0). The phase diagram in the 3D phase space of temperature, driving force amplitude, and frequency is investigated.

Correlation functions for a Bose-Einstein condensate in the Bogoliubov approximation

In this article we introduce a differential equation for the first order correlation function $G^{(1)}$ of a Bose-Einstein condensate at T=0. The Bogoliubov approximation is used. Our approach points out directly the dependence on the physical parameters. Furthermore it suggests a numerical method to calculate $G^{(1)}$ without solving an eigenvector problem. The $G^{(1)}$ equation is generalized to the case of non zero temperature.

Aging and non-linear glassy dynamics in a mean field model

The mean-field dynamics of a particle in a random, but short range correlated potential, offers the opportunity of observing both aging and driven stationary regimes. Using a geometrical approach previously introduced by the author, we study here the relation between these two situations, in the pure relaxational limit, i.e. the zero temperature case. In the stationary regime, the velocity(v) -force(f) characteristics is a power law, while the characteristic times scale like powers of v, in agreement with an early proposal by Horner. The cross-over between the aging, linear-response regime and the non linear stationary regime is smooth, and we propose a parametrisation of the correlation functions valid in both cases, by means of an "effective time". We conclude that aging and non linear response are dual manifestations of a single out-of-equilibrium state, which might be a generic situation.

Entropic rigidity of randomly diluted two- and three-dimensional networks.

In recent work, we presented evidence that site-diluted triangular central-force networks, at finite temperatures, have a nonzero shear modulus for all concentrations of particles above the geometric percolation concentration p(c). This is in contrast to the zero-temperature case where the (energetic) shear modulus vanishes at a concentration of particles p(r)>p(c). In the present paper we report on analogous simulations of bond-diluted triangular lattices, site-diluted square lattices, and site-diluted simple-cubic lattices. We again find that these systems are rigid for all p>p(c) and that near p(c) the shear modulus mu approximately (p-p(c))(f), where the exponent f approximately 1.3 for two-dimensional lattices and f approximately 2 for the simple-cubic case. These results support the conjecture of de Gennes that the diluted central-force network is in the same universality class as the random resistor network. We present approximate renormalization group calculations that also lead to this conclusion.

Fermionic atom laser

An output coupling of a magnetically trapped two-species Fermi gas to a untrapped species is considered which can be implemented using rf or optical Raman transitions. The process can be used to produce an intense output beam of fermionic atoms once the device reaches a threshold in the zero-temperature case. For finite temperatures there is no threshold, as the output current grows smoothly. This behavior, which is reminiscent of conventional optical and cavity-QED lasers, suggests the name fermionic atom laser for this device.

Topological susceptibility of QCD: From Minkowskian to Euclidean theory

We show how the topological susceptibility in the Minkowskian theory of QCD is related to the corresponding quantity in the Euclidean theory, which is measured on the lattice. We discuss both the zero-temperature case (T = 0) and the finite-temperature case (T > 0). It is shown that the two quantities are equal when T = 0, while the relation between them is much less trivial when T > 0. The possible existence of ``Kogut-Susskind poles'' in the matrix elements of the topological charge density between states with equal four-momenta turns out to invalidate the equality of these two quantities in a strict sense. However, an equality relation is recovered after one re-defines the Minkowskian topological susceptibility by using a proper infrared regularization.

Application of spin-dynamics methods to a study of magnetization tunneling in many-spin systems

Spin-dynamics methods were applied for the numerical study of magnetic tunneling in many-spin systems. A numerical technique based on the instanton approach was developed and the zero-temperature case as well as finite-temperature effects were considered. We show that even for a two-spin system results can differ considerably from those of a corresponding reduced one-spin (or collective spin) system. Moreover, it is argued that such a difference can take place for real materials such as magnetic molecules (e.g., Mn12). Thus, consideration of the many-spin nature of some systems is shown to be important.

Hadron masses in qQCD with Wilson fermions near the chiral limit

In quenched lattice QCD with standard Wilson fermions the quark propagator is computed very close to the chiral limit in the zero-temperature case. Starting from our experience with lattice QED we employ a modified statistical method in order to estimate reliably hadron masses. We discuss the implications for the mechanism of chiral symmetry breaking.

Stable States for Superconducting Systems with Combined S-Wave and D-Wave Pairing. Zero Temperature Case

The Fermi-liquid system with S-wave and D-wave pairing interaction harmonics is considered. The general equations for energy gap and thermo- dynamic potential difference for arbitrary temperatures are given. The de- tailed calculations are performed for zero-temperature limit. The obtained results are illustrated and discussed. The value and structure of energy gap are presented. It is showed that the anisotropic gap can be realized only for 90 <g2.

Cutting Rules at Finite Temperature

We discuss the cutting rules in the real-time approach to finite temperature field theory and show the existence of cancellations among classes of cut graphs which allows a physical interpretation of the imaginary part of the relevant amplitude in terms of the underlying microscopic processes. Furthermore, with these cancellations, any calculation of the imaginary part of an amplitude becomes much easier and completely parallel to the zero temperature case.

Variational Thomas-Fermi theory of a nonuniform Bose condensate at zero temperature

We derive a description of the spatially inhomogeneous Bose-Einstein condensate, treating the system locally as a homogeneous Bose gas. This approach, similar to the Thomas-Fermi model for the inhomogeneous many-particle fermion system, is well suited to describe the atomic Bose-Einstein condensates that have recently been obtained experimentally through atomic trapping and cooling. In this paper, we confine our attention to the zero-temperature case, although the treatment can be generalized to finite temperatures, as we shall discuss elsewhere. Several features of this approach, which we shall call the Thomas-Fermi-Bogoliubov description, are very attractive. (i) It is simpler than the Hartree-Fock-Bogoliubov technique. We can obtain analytical results in the case of weakly interacting bosons for quantities such as the chemical potential, the local depletion, pairing, pressure, and density of states. (ii) The method provides an estimate for the error due to the inhomogeneity of the Bose-condensed system. This error is a local quantity so that the validity of the description for a given trap and a given number of trapped atoms can be tested as a function of position. We see, for example, that at the edge of the condensate the Thomas-Fermi-Bogoliubov theory always breaks down. (iii) The Thomas-Fermi-Bogoliubov description can be generalized to treat the statistical mechanics of the Bose gas at finite temperatures.