Chemical thermalization in relativistic heavy ion collisions

We compute by numerical integration of the Dirac equation the number of quark-antiquark pairs initially produced in the classical color fields of colliding ultrarelativistic nuclei. While the number of pairs is parametrically suppressed in the coupling constant, we find that in this classical field model their production rate is comparable to the thermal ratio of gluons/pairs=9Nf/32. After isotropization one thus would have a quark-gluon plasma in chemical equilibrium.     

Threshold field in nucleation process for an inhomogeneous deformable nonlinear Klein-Gordon system

We investigate the effect of local inhomogeneity on the nucleation process of kink-antikink pairs in the driven nonlinear Klein-Gordon model with the Remoissenet-Peyrard substrate potential, whose shape can be varied as a function of the shape parameter and which has the sine-Gordon shape as a particular case. From numerical integrations of the model equations under defined conditions, the configuration of the critical nucleus in the presence of a localized inhomogeneity is determined and shown to be affected by the shape parameter of the substrate potential. The expression of the depinning threshold field of kink-antikink pairs, which is the value of the applied field at which the process of the nucleation of kink-antikink pairs takes place, is also obtained. The dependence of this depinning threshold field on the shape parameter r shows that it strongly increases, for small intensity of the impurity potential when the shape of the substrate potential deviates from the sinusoidal one.     

Nucleation and hysteresis in Ising model: classical theory versus computer simulation

We have studied the nucleation in the nearest neighbour ferromagnetic Ising model, in different (d) dimensions, by extensive Monte-Carlo simulation using the heat-bath dynamics. The nucleation time () has been studied as a function of the magnetic field (h) for various system sizes in different dimensions (d=2,3,4). The logarithm of the nucleation time is found to be proportional to the power (-(d-1)) of the magnetic field (h) in d dimensions. The size dependent crossover from coalescence to nucleation regime is observed in all dimensions. The distribution of metastable lifetimes are studied in both regions. The numerical results are compared and found to be consistent with the classical theoretical predictions. In two dimensions, we have also studied the dynamical response to a sinusoidally oscillating magnetic field. The reversal time is studied as a function of the inverse of the coercive field. The applicability of the classical nucleation theory to study the hysteresis and coercivity has been discussed. Received: 21 January 1998 / Accepted: 17 March 1998     

The two dimensional classical anisotropic Heisenberg ferromagnetic model with nearest- and next-nearest neighbor interactions

We use the self-consistent harmonic approximation (SCHA) to study the two-dimensional classical Heisenberg anisotropic (easy-plane) ferromagnetic model including nearest- and next-nearest neighbor exchange interactions. For temperatures much lower than the Kosterlitz-Thouless phase transition temperature T _KT, spin waves must be the most relevant excitations in the system and the SCHA must account for its behavior. However, for temperatures near T _KT, we should expect vortex pairs to be quite important. The effect of these vortex excitations on the phase transition temperature is included in our theory as a renormalization of the exchange interactions. Then, combining the SCHA theory to the renormalization effect due to vortex pairs, we calculate the dependence of T _KT as a function of the easy-plane anisotropies and exchange interactions. Received 3 April 2001 and Received in final form 20 September 2001     

Effective generation of polarization-entangled photon pairs in a cavity-QED system

We propose a cavity-QED scheme to effectively generate Einstein-Podolsky-Rosen polarization-entangled photon pairs. Assisted by a classical π-polarized pump field, a tripod four-level atom successively couples to two high-Q optical cavities possessing polarization degeneracy. Through stimulated Raman adiabatic passage process the polarization-entangled photon pairs can be produced.     

Non-classicality of photon added coherent and thermal radiations

Production and analysis of non-Gaussian radiation fields has evinced a lot of attention recently. Simplest way of generating such non-Gaussians is through adding (subtracting) photons to Gaussian fields. Interestingly, when photons are added to classical Gaussian fields, the resulting states exhibit non-classicality. Two important classical Gaussian radiation fields are coherent and thermal states. Here, we study the non-classical features of such states when photons are added to them. Non-classicality of these states shows up in the negativity of the Wigner function. We also work out the entanglement potential, a recently proposed measure of non-classicality for these states. Our analysis reveals that photon added coherent states are non-classical for all seed beam intensities; their non-classicality increases with the addition of more number of photons. Thermal state exhibits non-classicality at all temperatures, when a photon is added; lower the temperature, higher is their non-classicality.     

Pair Production in a Uniform Electric Field

We study the Klein-Gordon field coupled with an external uniform vector potential. We compute pair production in a finite time t using the semiclassical approximation, and show that, after the interaction of the Klein-Gordon field with the external potential, when 0 the average number of produced pairs is zero. There is agreement with the classical limit because the classical limit involves no production of pairs. We compared our results with those of Schwinger. Finally we saw that the random variable N(t)= net number of pairs produced at time t is in the semiclassical limit a stochastic Poisson process.     

A simple non-perturbative approach of atom ionisation by intense and ultra-short laser pulses

A simple theoretical approach based on Coulomb-Volkov states is introduced to predict ionisation of atoms by intense laser pulses in cases where the effective interaction time does not exceed one or two optical cycles [M. Nisoli et al., Opt. Lett. 22, 522 (1997)]. Under these conditions, the energy distributions of ejected electrons predicted by this non-perturbative approach are in very good agreement with “exact" results obtained by a full numerical treatment. The agreement is all the better that the principal quantum number of the initial state is high. For very strong fields, most electrons are ejected at an energy which is close to the classical kinetic energy that would be transferred to free electrons by the electromagnetic field during the pulse. The power of the present approach appears when keV. In this region, full numerical treatments become very lengthy and finally do not converge. However, the present Coulomb-Volkov theory still makes reliable predictions in very short computer times. Received 19 November 1999 and Received in final form 19 January 2000     

Fluid transport at low Reynolds number with magnetically actuated artificial cilia

By numerical modeling we investigate fluid transport in low-Reynolds-number flow achieved with a special elastic filament or artifical cilium attached to a planar surface. The filament is made of superparamagnetic particles linked together by DNA double strands. An external magnetic field induces dipolar interactions between the beads of the filament which provides a convenient way of actuating the cilium in a well-controlled manner. The filament has recently been used to successfully construct the first artificial micro-swimmer (R. Dreyfus et al., Nature 437, 862 (2005)). In our numerical study we introduce a measure, which we call pumping performance, to quantify the fluid transport induced by the magnetically actuated cilium and identify an optimum stroke pattern of the filament. It consists of a slow transport stroke and a fast recovery stroke. Our detailed parameter study also reveals that for sufficiently large magnetic fields the artificial cilium is mainly governed by the Mason number that compares frictional to magnetic forces. Initial studies on multi-cilia systems show that the pumping performance is very sensitive to the imposed phase lag between neighboring cilia, i.e., to the details of the initiated metachronal wave.     

Molecular many-body dissociation: Data reduction strategies in translational spectroscopy

Advanced time- and position-sensitive multi-hit detectors allow to study molecular breakup processes into two, three, and more massive fragments by translational spectroscopy. We discuss the feasibility to perform kinematically complete final state analysis of complex molecular dissociation processes using such detectors. We have developed new algorithms to determine - for an arbitrary number of fragments - the fragment momentum vectors in the center-of-mass frame from the measured positions and arrival time differences. These algorithms can easily be implemented to perform online data reduction in coincidence experiments. We have tested the new data reduction strategies in an experimental study and in Monte-Carlo simulations of realistic experimental conditions. We show that the new algorithms can discriminate between two-, three-, and four-body decay of a four-atomic molecule and can uniquely determine the momentum vectors of all fragments. For two-body decay, we find that the accuracy of the new algorithm is superior to the frequently used approximate formula introduced by DeBruijn and Los. We demonstrate this improvement in the evaluation of experimental data for the decay of laser-excited triatomic hydrogen H₃ 3s (N=1,K=0) into H + H₂(v,J) fragment pairs. Received 12 April 2000     

Exact Bures probabilities that two quantum bits are classically correlated

In previous studies, we have explored the ansatz that the volume elements of the Bures metrics over quantum systems might serve as prior distributions, in analogy with the (classical) Bayesian role of the volume elements (“Jeffreys' priors”) of Fisher information metrics. Continuing this work, we obtain exact Bures prior probabilities that the members of certain low-dimensional subsets of the fifteen-dimensional convex set of density matrices are separable or classically correlated. The main analytical tools employed are symbolic integration and a formula of Dittmann (J. Phys. A 32, 2663 (1999)) for Bures metric tensors. This study complements an earlier one (J. Phys. A 32, 5261 (1999)) in which numerical (randomization) - but not integration - methods were used to estimate Bures separability probabilities for unrestricted and density matrices. The exact values adduced here for pairs of quantum bits (qubits), typically, well exceed the estimate () there, but this disparity may be attributable to our focus on special low-dimensional subsets. Quite remarkably, for the q= 1 and states inferred using the principle of maximum nonadditive (Tsallis) entropy, the Bures probabilities of separability are both equal to . For the Werner qubit-qutrit and qutrit-qutrit states, the probabilities are vanishingly small, while in the qubit-qubit case it is . Received 10 December 1999 and Received in final form 24 February 2000     

Ground-state energy of a classical artificial molecule

We study the ground-state energy of a classical artificial molecule formed by two-dimensional clusters (artificial atoms) of N/2 charged particles separated by a distance d. For the small molecules of N = 2 and 4, we obtain analytical expressions for this energy. For the larger ones, we calculate the ground-state energy using molecular dynamics simulation for N up to 128. From our numerical results, we are able to find out a function to approximate the ground-state energy of the molecules covering the range from atoms to molecules for any inter-atom distance d and for particle number from N = 8 to 128 within a difference less than one percent from the MD data.     

Electromagnetically induced transparency and evolution of a two-level system under chaotic field of arbitrary intensity

The electromagnetically induced transparency (EIT) with a (near-)resonant chaotic (amplitude-phase fluctuating, Gaussian-Markovian) coupling field is studied theoretically. The Fourier transform of the steady-state EIT spectrum, which determines a nonstationary probe absorption, is also considered. This quantity equals the average diagonal element of the (reduced) evolution operator of the coupled transition (the evolution function). The exact solution in the form of a continued fraction is obtained and used to perform numerical calculations. Moreover, a number of approximate analytical results are obtained, which, together with the results of previous publications, describe the EIT and the evolution function in all possible regimes. In particular, in the constructive-interference case the EIT increases with the coupling-field bandwidth ν at sufficiently small ν. For a strong field, the maximum of the transparency as a function of ν is less than that for a monochromatic field of the same average intensity. In contrast, for a weak field, there is a range of ν values, where the field fluctuations do not affect the EIT. The latter result is shown to hold for a broad class of stochastic fields. Received 31 December 2000 and Received in final form 14 May 2001     

Signals of a Weibel instability in the melting color glass condensate

Based on our work hep-ph/0510121, we discuss further the numerical study of classical SU(2) 3+1-D Yang-Mills equations for matter produced in a high-energy heavy-ion collision. The growth of the amplitude of fluctuations as exp(Γ ) (where g ²μ is a scale arising from the saturation of gluons in the nuclear wave function) is shown to be robust over a wide range of initial amplitudes that violate boost invariance. We argue that this growth is due to a non-Abelian Weibel instability, the scale of which is set by a dynamically generated plasmon mass. We discuss the relation of Γ to the prediction from kinetic theory.     

Internal structure of a quantum soliton and classical excitations due to trap opening

We analytically solve two problems that may be useful in the context of the recent observation of matter wave bright solitons in a one-dimensional attractive atomic Bose gas. The first problem is strictly beyond mean field: from the Bethe ansatz solution we extract the internal correlation function of the particle positions in the quantum soliton, that is for a fixed center of mass position. The second problem is solved in the limit of a large number of particles, where the mean field theory is asymptotically correct: it deals with the number of excitations created by the opening of the trap, starting from a pure soliton in a weakly curved harmonic potential.     

Quantum fluctuations in a scale-free network-connected Ising system

We study the effect of quantum fluctuations in an Ising spin system on a scale-free network of degree exponent γ>5 using a quantum Monte Carlo simulation technique. In our model, one can adjust the magnitude of the magnetic field perpendicular to the Ising spin direction and can therefore control the strength of quantum fluctuations for each spin. Our numerical analysis shows that quantum fluctuations reduce the transition temperature T_c of the ferromagnetic-paramagnetic phase transition. However, the phase transition belongs to the same mean-field type universality class both with and without the quantum fluctuations. We also study the role of hubs by turning on the quantum fluctuations exclusively at the nodes with the most links. When only a small number of hub spins fluctuate quantum mechanically, T_c decreases with increasing magnetic field until it saturates at high fields. This effect becomes stronger as the number of hub spins increases. In contrast, quantum fluctuations at the same number of “non-hub” spins do not affect T_c. This implies that the hubs play an important role in maintaining order in the whole network.     

Kink solutions of the classical transverse field Ising chain

We investigate stationary and travelling wave solutions of the classical one-dimensional transverse field Ising model. Results are given on the existence, shape and stability of kink solutions and periodic solutions. We review recent analytical results (e.g., the proof of existence of a one-parameter family of stationary kink solutions and the proof of existence of travelling wave kink solutions with nonzero velocity c≠ 0) and extend them by the use of numerical methods. Small oscillations arising in the tails of travelling kink solutions are investigated numerically. In the end, stability analysis puts some light on pinning effects. Received 23 February 2001 and Received in final form 4 October 2001     

Femtosecond pump-probe fluorescence signals from classical trajectories: comparison with wave-packet calculations

A classical approach to simulate femtosecond pump-probe experiments is presented and compared to the quantum mechanical treatment. We restrict the study to gas-phase systems using the I₂ molecule as a numerical example. Thus, no relaxation processes are included. This allows for a direct comparison between purely quantum mechanical results and those obtained from classical trajectory calculations. The classical theory is derived from the phase-space representation of quantum mechanics. Various approximate quantum mechanical treatments are compared to their classical counterparts. Thereby it is demonstrated that the representation of the radial density as prepared in the pump-process is most crucial to obtain reliable signals within the classical approach. Received 28 March 2001     

The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single-particle levels of a potential well (mean field) and interacting through a pairing force in the framework of the Richardson equations. The associated solutions are classified in terms of a number v_l, which reduces to the seniority v in the limit of a large pairing strength G and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the G limit. We express analytically, through the moments of the single-particle levels distribution, the collective mode energy and the two critical values G_cr⁺ and G_cr^- of the coupling which can exist on a single-particle level with no pair degeneracy. Notably G_cr⁺ and G_cr^-, when the number of single particle levels goes to infinity, merge into the critical coupling of a one-pair system G_cr (when it exists), which is not envisioned by the Richardson theory. In correspondence of G_cr, the system undergoes a transition from a mean-field- to a pairing-dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes versus G finding out that the former, for G > G_cr^-, come close to the BCS predictions, whereas the latter display a divergence at G_cr, signaling the onset of a long-range off-diagonal order in the system.