Rotating matter waves in Bose-Einstein condensates

In this paper we consider analytically and numerically the dynamics of waves in two-dimensional, magnetically trapped Bose-Einstein condensates in the weak interaction limit. In particular, we consider the existence and stability of azimuthally modulated structures such as rings, multi-poles, soliton necklaces, and vortex necklaces. We show how such structures can be constructed from the linear limit through Lyapunov-Schmidt techniques and continued to the weakly nonlinear regime. Subsequently, we examine their stability, and find that among the above solutions the only one which is always stable is the vortex necklace. The analysis is given for both attractive and repulsive interactions among the condensate atoms. Finally, the analysis is corroborated by numerical bifurcation results, as well as by numerical evolution results that showcase the manifestation of the relevant instabilities.     

Towards exotic nuclear matter

In this article I would like to describe what I am doing right now. First, introductory remarks on nuclear matter at high densities and/or high temperatures are presented. Then, I report our recent data obtained at the Brookhaven AGS. Finally, I describe briefly our future RHIC experiment, PHENIX.     

Superfluid nuclear matter calculations

We present a method to calculate nuclear matter properties in the superfluid phase. The method is based on the use of self-consistent off-shell nucleon propagators in the T-matrix equation. Such a complete treatment of the spectral function is required below and around T_c due to a pseudogap formation in the spectral function. In the superfluid phase we introduce the anomalous self-energy in the fermion propagators and in the T-matrix equation, consistently with the strong coupling BCS equations. The equations for the nucleon spectral function include both a contribution of condensed and scattering pairs. The method is illustrated by numerical calculations. Above T_c pseudogap formation is visible in the spectral function and below T_c a superfluid gap also appears.     

Skyrmion in nuclear matter

The properties of Skyrmions in finite nuclei are considered. The deformation effect is taken into account through the external-field-induced distortion of the profile function of a chiral field. The masses of classical Skyrmions and the distribution of their baryon number versus the Skyrmion position within a nucleus are discussed.     

Properties of nuclear S-wave matter

Comparative Brueckner and Jastrow studies of the properties of nuclear matter are somewhat hampered by the complexities of realistic nucleon-nucleon potentials. To avoid some of these difficulties we investigate a nuclear matter model called S-wave matter, which consists of nucleons interacting via various of the Aviles S-wave delta function potentials. These potentials all fit the two-body S-wave scattering data for energies up to 500 meV. By using Jastrow methods we find two-body contributions to the ground state energy ranging from 18 to 29 MeV, depending on the particular potential used; the results for a given potential are in good agreement with the Brueckner results of Haftel. In addition, there are significant Jastrow three-body contributions, indicating that the equivalent three-body Brueckner contributions should be evaluated.     

Alpha-particle model for nuclear matter

Infinite nuclear matter is assumed to be composed of an equal even number of protons and neutrons. The surface region of nuclear matter is replaced by an assembly of alpha-particles interacting through a potential composed of a strong short-range repulsion and a weak long-range attraction of the Gaussian form. The energy gap in nuclear matter and the effective mass of alpha particles have been calculated. The result shows that the energy gap is more than 2 MeV but 5 MeV. The ratio of the effective mass m* to the free particle mass m of alpha-particles is always greater than unity and its maximum value is a little over 5. For an assembly of alpha-particles to be stable, it must be a dilute weakly interacting assembly. The net interaction must be repulsive and the nuclear density should be less than the saturation limit. The results have been compared with previous calculations.The author is very grateful to Prof. B. R. Seth, Prof. A. M. Sessler and Prof. S. Duttamazumdar for encouragement and helpful discussions.     

Quantum condensates in nuclear matter

Nonrelativistic nuclear matter is considered as a special example of a many-particle system. Quantum statistical methods are applied to treat the formation and dissolution of bound states in dense matter. The formation of quantum condensates is investigated. Special aspects are the transition from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) pairing as well as the occurrence of quartetting. Consequences for the structure of nuclei are compared with experimental data. Exercises to illustrate the main features of in-medium effects in nuclear matter are given. The text was submitted by the author in English.     

Hot nuclear matter with dilatons

We study hot nuclear matter in a model based on nucleon interactions deriving from the exchange of scalar and vector mesons. The main new feature of our work is the treatment of the scale breaking of quantum chromodynamics through the introduction of a dilaton field. Although the dilaton effects are quite small quantitatively, they affect the high-temperature phase transition appreciably. We find that inclusion of the dilaton leads to a metastable high-density state at zero pressure, similar to that found by Glendenning who considered instead the admixture of higher baryon resonances.     

The disassembly of nuclear matter

A statistical model is applied for multi-fragment final states in nuclear collisions with bombarding energies E/A ≈ 100 MeV. A portion of the intermediate system formed is assumed to decay according to the available classical non-relativistic phase space, calculated in a grand canonical ensemble. The model correlates and predicts many experimental observables in terms of three parameters: the available energy per nucleon, the isospin asymmetry, and the effective interaction volume.     

Many-body theory of nuclear matter

We combine the many-body theory and the low-density expansion developed by Brueckner, Bethe and others to investigate several properties of the ground state and of single-particle excited states of symmetric nuclear matter. We calculate the following quantities from Reid's hard core nucleon-nucleon interaction: strength, energy-dependence, nonlocality and density-dependence of the real and of the imaginary parts of the optical-model potential, momentum distribution in the interacting ground state, dependence on density and momentum of the norm of a quasiparticle and of the effective mass, spectral function for particle states, saturation density and average binding energy per nucleon. No free parameter is adjusted in the calculation; good agreement is obtained with empirical values. It is shown that the effective mass has a narrow maximum at the Fermi surface; this is investigated in the framework of analytical models.     

Phase transitions in nuclear matter

The possible phases of nuclear matter are summarised. A new periodic phase of nuclear matter is discussed in details. In this phase the nucleon spin orientation follows the direction of the magnetic field associated with the periodic vector meson field. The probability of the transition accompanied by gamma radiation between this periodic phase and the anisotropic normal phase is derived.     

Static viscosity of nuclear matter

The static shear viscosity η₀ of symmetric nuclear matter is estimated. It is found, that for reasonable nuclear temperatures the mean free path connected with η_o is considerably larger than the nuclear radii. We therefore conclude, that the concept of viscosity cannot be applied to nuclear fission and heavy ion collisions without taking into account the nuclear surface.     

Excitation spectrum for nuclear matter

Properties of an infinite nuclear matter of interacting alpha-particle have been studied. The expression obtained for the excitation spectrum exhibits the existence of the energy gap in the nuclear matter. The energy gap changes withm _* /m , the ratio between effective and true mass of an alpha-particle, and it seems to disappear for higher values ofm _* /m .On leave of absence fromK.G.K. College, Moradabad (U.P.) India.We are highly thankful to Prof. S. Duttamajumdar for valuable comments, and to the Indian National Science Academy, New Delhi, for financial assistance.     

D-mesons in dense nuclear matter

The D-meson properties in dense nuclear matter are studied. The D-meson spectral density is obtained within the framework of a coupled-channel self-consistent calculation, assuming as bare meson-baryon interaction a separable potential. The resonance is generated dynamically in our coupled-channel model. The medium modifications of the D-meson properties due to Pauli blocking and the dressing of D-mesons, nucleons and pions are also studied. We conclude that the self-consistent coupled-channel process reduces the in-medium effects on the D-meson compared to previous literature which did not consider the coupled-channel structure.Received: 14 January 2005, Published online: 31 May 2005PACS: 14.40.Lb, 14.20.Gk, 21.65. + f     

Optical potential and nuclear matter

The relation of the parameters of the optical nucleon-nucleus potential to the characteristics of nuclear matter is established. The existing values of the parameters of the optical potential reflect well the binding energy per nucleon and the symmetry energy of nuclear matter. It is shown that the theorem of Hugenholtz and van Hove is not valid for the real part of the optical potential.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–100, January, 1978.     

Collective excitations of nuclear matter

It has been shown that in a renormalizable gauge-invariant field-theory model, besides the usual factorizable contribution to the parity-violating vector-meson-exchange potential there is a nonseparable contribution which is equally important. Both contributions have been calculated in the model based on the Bethe-Salpeter equation which describes vector mesons as bound quark-antiquark states. Complete expressions for parity-violating nuclear potentials have been given for the Cabibbo and the Weinberg-Salam models, including the asymptotically-free field-theory version of the latter, which employs coloured quarks and vector gluons.     

Pion superfluidity in nuclear matter

We utilize analogies with theories and properties of both liquid He⁴ and electrons in solids and liquids in constructing a model of nuclear matter in which the presence of stabilized pions is assumed. This model is then used to predict relationships between various thermodynamic parameters of a nuclear matter system, such as that between its “free” pion density and the characteristic transition temperature at which a Bose-Einstein condensation will commence.