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We contrast {\it four} distinct versions of the BCS-Bose statistical crossover theory according to the form assumed for the electron-number equation that accompanies the BCS gap equation. The four versions correspond to explicitly accounting for two-hole-(2h) as well as two-electron-(2e) Cooper pairs (CPs), or both in equal proportions, or only either kind. This follows from a recent generalization of the Bose-Einstein condensation (GBEC) statistical theory that includes not boson-boson interactions but rather 2e- and also (without loss of generality) 2h-CPs interacting with unpaired electrons and holes in a single-band model that is easily converted into a two-band model. The GBEC theory is essentially an extension of the Friedberg-T.D. Lee 1989 BEC theory of superconductors that excludes 2h-CPs. It can thus recover, when the numbers of 2h- and 2e-CPs in both BE-condensed and noncondensed states are separately equal, the BCS gap equation for all temperatures and couplings as well as the zero-temperature BCS (rigorous-upper-bound) condensation energy for all couplings. But ignoring either 2h- {\it or} 2e-CPs it can do neither. In particular, only {\it half} the BCS condensation energy is obtained in the two crossover versions ignoring either kind of CPs. We show how critical temperatures $T_{c}$ from the original BCS-Bose crossover theory in 2D require unphysically large couplings for the Cooper/BCS model interaction to differ significantly from the $T_{c}$s of ordinary BCS theory (where the number equation is substituted by the assumption that the chemical potential equals the Fermi energy)., thirteen pages including two figures. Physica C (in press, 2007)

Made available in DSpace on 2018-11-26T16:17:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-10-29 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) We demonstrate a robust, stable, mobile, two-dimensional (2D) spatial and three-dimensional (3D) spatiotemporal optical soliton in the core of an optical vortex, while all nonlinearities are of the cubic (Kerr) type. The 3D soliton can propagate with a constant velocity along the vortex core without any deformation. Stability of the soliton under a small perturbation is established numerically. Two such solitons moving along the vortex core can undergo a quasielastic collision at medium velocities. Possibilities of forming such a 2D spatial soliton in the core of a vortical beam are discussed. Univ Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, SP, Brazil Univ Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, SP, Brazil FAPESP: 2012/00451-0 CNPq: 303280/2014-0

Made available in DSpace on 2018-12-11T16:58:04Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-08-12 We demonstrate that the ground state of a trapped spin-1 and spin-2 spinor ferromagnetic Bose-Einstein condensate (BEC) can be well approximated by a single decoupled Gross-Pitaevskii (GP) equation. Useful analytic models for the ground-state densities of ferromagnetic BECs are obtained from the Thomas-Fermi approximation (TFA) to this decoupled equation. Similarly, for the ground states of spin-1 antiferromagnetic and spin-2 antiferromagnetic and cyclic BECs, some of the spin-component densities are zero, which reduces the coupled GP equation to a simple reduced form. Analytic models for ground-state densities are also obtained for antiferromagnetic and cyclic BECs from the TFA to the respective reduced GP equations. The analytic densities are illustrated and compared with the full numerical solution of the GP equation with realistic experimental parameters. Instituto de Física Teórica, Universidade Estadual Paulista - UNESP Instituto de Física Teórica, Universidade Estadual Paulista - UNESP

State-selected total cross sections and thermal rate coefficients are computed for the HD + $ortho$-/$para$-H$_2$ rotational energy transfer collision at low temperatures: 2 K $\lesssim$ T $\lesssim$ 300 K. A modified H$_2$-H$_2$ potential energy surface (PES) devised by Hinde is used for this pure quantum-mechanical dynamical computation. A comparison of the new results for the HD + $ortho$-/$para$-H$_2$ scattering problem and previous calculations computed with the use of other older PESs is presented and discussed., Revtex preprint: 34 pages, 3 tables and 16 figures

Made available in DSpace on 2018-12-11T16:57:48Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-06-15 Five-component minimum-energy bound states and mobile vector solitons of a spin-orbit-coupled quasi-one-dimensional hyperfine-spin-2 Bose-Einstein condensate are studied using the numerical solution and variational approximation of a mean-field model. Two distinct types of solutions with single-peak and multipeak density distribution of the components are identified in different domains of interaction parameters. From an analysis of Galilean invariance and time-reversal symmetry of the Hamiltonian, we establish that vector solitons with multipeak density distribution preserve time-reversal symmetry, but they cannot propagate while maintaining the shape of individual components. However, those with single-peak density distribution violate time-reversal symmetry of the Hamiltonian, but they can propagate with a constant velocity and maintain the shape of individual components. Instituto de Física Teórica, Universidade Estadual Paulista, UNESP Instituto de Física Teórica, Universidade Estadual Paulista, UNESP

Employing a time-dependent mean-field-hydrodynamic model we study the generation of black solitons in a degenerate fermion-fermion mixture in a cigar-shaped geometry using variational and numerical solutions. The black soliton is found to be the first stationary vibrational excitation of the system and is considered to be a nonlinear continuation of the vibrational excitation of the harmonic oscillator state. We illustrate the stationary nature of the black soliton, by studying different perturbations on it after its formation., 7 pages, 10 figures

We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic dark solitons in a trapped degenerate fermi gas mixed with a Bose-Einstein condensate in a harmonic as well as a periodic optical-lattice potential. The dark soliton with a "notch" in the probability density with a zero at the minimum is simulated numerically as a nonlinear continuation of the first vibrational excitation of the linear mean-field-hydrodynamic equations, as suggested recently for pure bosons. We study the free expansion of these dark solitons as well as the consequent increase in the size of their central notch and discuss the possibility of experimental observation of the notch after free expansion., Comment: 14 pages, 6 figures

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation for attractive interaction (with cubic or Kerr nonlinearity) we show that a stable bound state can appear in a Bose-Einstein condensate (BEC) in a localized exponentially-screened radially-symmetric harmonic potential well in two and three dimensions. We also consider an axially-symmetric configuration with zero axial trap and a exponentially-screened radial trap so that the resulting bound state can freely move along the axial direction like a soliton. The binding of the present states in shallow wells is mostly due to the nonlinear interaction with the trap playing a minor role. Hence these BEC states are more suitable to study the effect of the nonlinear force on the dynamics. We illustrate the highly nonlinear nature of breathing oscillation of these states. Such bound states could be created in BECs and studied in the laboratory with present knowhow., Comment: 16 pages, 13 ps figures, Journal of Physics B

We study the expansion of a Bose-Einstein condensate trapped in a combined optical-lattice and axially-symmetric harmonic potentials using the numerical solution of the mean-field Gross-Pitaevskii equation. First, we consider the expansion of such a condensate under the action of the optical-lattice potential alone. In this case the result of numerical simulation for the axial and radial sizes during expansion is in agreement with two experiments by Morsch et al.[2002 Phys. Rev. A 66 021601(R) and 2003 Laser Phys. 13 594]. Finally, we consider the expansion under the action of the harmonic potential alone. In this case the oscillation and the disappearance and revival of the resultant interference pattern is in agreement with the experiment by M\"uller et al. [2003 J. Opt. B 5 538]., Comment: 10 pages, 14 ps and eps figures

We analyze the localization of a Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasi-periodic optical-lattice potential by numerically solving the 1D Gross-Pitaevskii equation (1D GPE). We first derive the 1D GPE from the dimensional reduction of the 3D quantum field theory of interacting bosons obtaining two coupled differential equations (for axial wavefuction and space-time dependent transverse width) which reduce to the 1D GPE under strict conditions. Then, by using the 1D GPE we report the suppression of localization in the interacting BEC when the repulsive scattering length between bosonic atoms is sufficiently large., Comment: 10 pages, 2 figures, presented at the 7th Workshop on Quantum Chaos and Localisation Phenomena, May 29-31, 2015 - Warsaw, Poland; to be published in a special issue of Acta Physica Polonica A

Made available in DSpace on 2022-04-29T07:25:49Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-01-23 We study the ground-state density profile of a spin-orbit-coupled f=2 spinor condensate in a quasi-one-dimensional trap. The Hamiltonian of the system is invariant under time reversal but not under parity. We identify different parity- and time-reversal symmetry-breaking states. The time-reversal symmetry breaking is possible for degenerate states. A phase separation among densities of different components is possible in the domain of time-reversal symmetry breaking. Different types of parity- and time-reversal symmetry-breaking states are predicted analytically and studied numerically. We employ numerical and approximate analytic solutions of a mean-field model in this investigation to illustrate our findings. Instituto de Física Teórica, Universidade Estadual Paulista Instituto de Física Teórica, Universidade Estadual Paulista

Many of the static and dynamic properties of an atomic Bose-Einstein condensate (BEC) are usually studied by solving the mean-field Gross-Pitaevskii (GP) equation, which is a nonlinear partial differential equation for short-range atomic interaction. More recently, BEC of atoms with long-range dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integro-differential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and non-stationary solutions of the full three-dimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one- (1D) and two-dimensional (2D) GP equations satisfied by cigar- and disk-shaped dipolar BECs. We employ the split-step Crank-Nicolson method with real- and imaginary-time propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x-y and x-z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, root-mean-square sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and Thomas-Fermi approximations., Comment: To download the programs click other and download source

The effects of a sudden increase and decrease of the interatomic interaction and harmonic-oscillator trapping potential on vortices in a quasi two-dimensional rotating Bose-Einstein condensate are investigated using the mean-field Gross-Pitaevskii equation. Upon increasing the strength of interaction suddenly the condensate enters a nonstationary oscillating phase which starts to develop more vortices. The opposite happens if the strength is reduced suddenly. Eventually, the number of vortices attains a final value at large times. Similarly, the number of vortices increases (decreases) upon a sudden reduction (augmentation) in the trapping potential. We also study the decay of vortices when the rotation of the condensate is suddenly stopped. Upon a free expansion of a rotating BEC with vortices the radius of the vortex core increases more rapidly than the radius of the condensate. This makes the counting and detection of multiple vortex easier after a free expansion., RevTeX 4, 7 pages, 7 EPS figures

Direct muon transfer in low-energy collisions of the muonic hydrogen H$_\mu$ and helium (He$^{++}$) is considered in a three-body quantum-mechanical framework of coordinate-space integro-differential Faddeev-Hahn-type equations within two- and six-state close coupling approximations. The final-state Coulomb interaction is treated without any approximation employing appropriate Coulomb waves in the final state. The present results agree reasonably well with previous semiclassical calculations., Comment: 4 revtex4 pages

The low-energy scattering of ortho positronium (Ps) by ortho Ps has been studied in a full quantum mechanical coupled-channel approach. In the singlet channel (total spin $s_T=0$) we find S- and P-wave resonances at 3.35 eV (width 0.02 eV) and 5.05 eV (width 0.04 eV), respectively and a binding of 0.44 eV of Ps$_2$. The scattering length for $s_T=0$ is 3.95 \AA and for $s_T=2$ is 0.83 \AA . The small $s_T=2$ scattering length makes the spin-polarized ortho Ps atoms an almost noninteracting ideal gas which may undergo Bose-Einstein condensation., Comment: 8 Latex pages, 4 post-script figures

We demonstrate stable, robust, bright dipolar Bose-Einstein condensate (BEC) solitons, moving in a direction perpendicular to the polarization direction, formed due to dipolar interaction for repulsive contact interaction. At medium velocity the head on collision of two such solitons is found to be quasi elastic with practically no deformation. Upon small perturbation the solitons are found to exhibit sustained breathing oscillation. The findings are illustrated by numerical simulation using the 3D mean-field Gross-Pitaevskii equation and a reduced 2D model in three and two spatial dimensions employing realistic interaction parameters for a dipolar $^{164}$Dy BEC., Comment: arXiv admin note: text overlap with arXiv:1404.1946

Made available in DSpace on 2022-04-29T07:16:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-06-03 National Natural Science Foundation of China We study the localization of a noninteracting and weakly interacting Bose-Einstein condensate (BEC) with spin-orbit coupling loaded in a quasiperiodic bichromatic optical lattice potential using the numerical solution and variational approximation of a binary mean-field Gross-Pitaevskii equation with two pseudospin components. We confirm the existence of the stationary localized states in the presence of the spin-orbit and Rabi couplings for an equal distribution of atoms in the two components. We find that the interaction between the spin-orbit and Rabi couplings favors the localization or delocalization of the BEC depending on the phase difference between the components. We also studied the oscillation dynamics of the localized states for an initial population imbalance between the two components. © 2014 American Physical Society. Department of Physics, Hubei Normal University, Huangshi 435002 Instituto de Física Teórica, Universidade Estadual Paulista, 01.140-070 São Paulo, São Paulo Instituto de Física Teórica, Universidade Estadual Paulista, 01.140-070 São Paulo, São Paulo National Natural Science Foundation of China: 11274104

We demonstrate robust, stable, mobile, quasi-one-dimensional, dark-in-bright dipolar Bose-Einstein condensate (BEC) soliton with a notch in the central plane formed due to dipolar interaction for repulsive contact interaction. At medium velocity the head on collision of two such solitons is found to be quasi elastic with practically no deformation. A proposal for creating dipolar dark-in-bright solitons in laboratories by phase imprinting is also discussed. A rich variety of such solitons can be formed in dipolar binary BEC, where one can have a dark-in-bright soliton coupled to a bright soliton or two coupled dark-in-bright solitons. The findings are illustrated using numerical simulation in three spatial dimensions employing realistic interaction parameters for a dipolar 164Dy BEC and a binary 164Dy-162Dy BEC., arXiv admin note: text overlap with arXiv:1401.3184

Made available in DSpace on 2018-12-11T16:58:12Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-04-14 We study the Josephson oscillation and self-trapping dynamics of a cigar-shaped dipolar Bose-Einstein condensate of 52Cr atoms polarized along the symmetry axis of an axially symmetric double-well potential using the numerical solution of a mean-field model, for dominating repulsive contact interaction (large positive scattering length a) over an anisotropic dipolar interaction. Josephson-type oscillation emerges for small and very large numbers of atoms, whereas self-trapping is noted for an intermediate number of atoms. The dipolar interaction pushes the system away from self-trapping towards Josephson oscillation. We consider a simple two-mode description for a qualitative understanding of the dynamics. © 2014 American Physical Society. Instituto de Física Teórica, UNESP-Universidade Estadual Paulista, 01.140-070 São Paulo, São Paulo Instituto de Física Teórica, UNESP-Universidade Estadual Paulista, 01.140-070 São Paulo, São Paulo

A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and three dimensions. The present discussion illustrates in a simple fashion the concept of partial-wave decomposition, Green's function, Lippmann-Schwinger integral equations of scattering for wave function and transition operator, optical theorem and unitarity relation. We illustrate the present approach with a Dirac delta potential., 12 pages, accepted in American Journal of Physics

Scattering of ortho positronium (Ps) by cesium and rubidium atoms has been investigated employing a three-Ps-state coupled-channel model with Ps(1s,2s,2p) states using a time-reversal-symmetric regularized electron-exchange model potential. We find a narrow S-wave singlet resonance at 5.057 eV of width 0.003 eV in the Ps-Rb system and at 5.067 eV of width 0.003 eV in the Ps-Cs system. Singlet P-wave resonances in both systems are found at 5.3 eV of width 0.4 eV. Singlet D-wave structures are found at 5.4 eV in both systems. The pronounced P- and D-wave resonances in these systems lead to easily detectable local minima in the low-energy elastic cross sections. We also report results for elastic and Ps-excitation cross sections for Ps scattering by Rb and Cs., Comment: 8 pages, 5 figures

Bose-Einstein condensation (BEC) in two dimensions (2D) (e.g., to describe the quasi-2D cuprates) is suggested as the possible mechanism widely believed to underlie superconductivity in general. A crucial role is played by nonzero center-of-mass momentum Cooper pairs (CPs) usually neglected in BCS theory. Also vital is the unique {\it linear} dispersion relation appropriate to weakly-coupled "bosonic" CPs moving in the Fermi sea--rather than in vacuum where the dispersion would be quadratic but only for very strong coupling, and for which BEC is known to be impossible in 2D., Comment: 6 pages included 3 figures

We study the elastic scattering of positronium atoms by hydrogen atoms at medium energies using partial-wave Born-Oppenheimer (BO) exchange amplitudes and report accurate BO cross sections in the energy range 0 to 60 eV. The present BO results agree with a 22-state R-matrix and a five-state coupled-channel model potential calculation, but disagree strongly with a conventional close-coupling calculation as well as its input BO amplitudes at medium energies.

Submitted by Vitor Silverio Rodrigues (vitorsrodrigues@reitoria.unesp.br) on 2014-05-27T11:19:59Z No. of bitstreams: 0Bitstream added on 2014-05-27T14:45:07Z : No. of bitstreams: 1 2-s2.0-0034207355.pdf: 149291 bytes, checksum: b402b628f6cd57af18851a24e80416db (MD5) Made available in DSpace on 2014-05-27T11:19:59Z (GMT). No. of bitstreams: 0 Previous issue date: 2000-12-01 A nonthermal quantum mechanical statistical fragmentation model based on tunneling of particles through potential barriers is studied in compact two- and three-dimensional systems. It is shown that this fragmentation dynamics gives origin to several static and dynamic scaling relations. The critical exponents are found and compared with those obtained in classical statistical models of fragmentation of general interest, in particular with thermal fragmentation involving classical processes over potential barriers. Besides its general theoretical interest, the fragmentation dynamics discussed here is complementary to classical fragmentation dynamics of interest in chemical kinetics and can be useful in the study of a number of other dynamic processes such as nuclear fragmentation. ©2000 The American Physical Society. Departamento de Física Universidade Federal de Pernambuco, 50670-901 Recife-PE Inst. de Fis. Teórica Universidade Estadual Paulista, 01405-900 São Paulo, SP Laboratory for Theoretical Physics Inst. for Nucl. Sci. Vinča, P. O. Box 522, YU-11001 Belgrade Inst. de Fis. Teórica Universidade Estadual Paulista, 01405-900 São Paulo, SP

The temperature dependencies of specific heat and spin susceptibility of a coupled $d_{x^2-y^2} +id_{xy}$ superconductor in the presence of a weak $d_{xy}$ component are investigated in the tight-binding model (1) on square lattice and (2) on a lattice with orthorhombic distortion. As the temperature is lowered past the critical temperature $T_c$, first a less ordered $d_{x^2-y^2}$ superconductor is created, which changes to a more ordered $d_{x^2-y^2} +id_{xy}$ superconductor at $T_{c1} (

We derive a closed-form analytic expression in momentum space for the asymptotic non-hydrogenic wavefunction of the quantum defect theory (QDT) due to Seaton and compare it with a widely used QDT-approximate wavefunction for the Rydberg states (2s), (6s) and (5s)

The temperature dependencies of specific heat and spin susceptibility of a coupled $d_{x^2-y^2} +id_{xy}$ superconductor in the presence of a weak $d_{xy}$ component are investigated in the tight-binding model (1) on square lattice and (2) on a lattice with orthorhombic distortion. As the temperature is lowered past the critical temperature $T_c$, first a less ordered $d_{x^2-y^2}$ superconductor is created, which changes to a more ordered $d_{x^2-y^2} +id_{xy}$ superconductor at $T_{c1} (, Comment: Latex file, 11 pages, 7 postscript figures

An experimental study of fragmentation of brittle solids under the application of repeated impulsive force is made, emphasizing the behavior of the diversity of fragments. Several scaling relations involving diversity and number of fragments are obtained from experiments and the results are compared with computer simulations.

The Gel'fand-Levitan formalism is used to study how a selected set of bound states can be eliminated from the spectrum of the Coulomb potential and also how to construct a bound state in the Coulomb continuum. It is demonstrated that a sizeable quantum well can be produced by deleting a large number of levels from the s spectral series and the edge of the Coulomb potential alone can support the von Neumann-Wigner states in the continuum.

We perform a three-positronium (Ps) state [Ps(1s,2s,2p)] coupled-channel calculation of scattering including the effect of electron exchange. At medium energies, higher excitations and ionization of Ps are treated within the framework of the first Born approximation. In both cases exchange is included using a recently proposed nonlocal model exchange potential which is free of non-orthogonality problems common in the usual antisymmetrization scheme. The present total cross sections at low and medium energies are in encouraging agreement with experiment.

It is shown that the appearance of a fixed-point singularity in the kernel of the two-electron Cooper problem is responsible for the formation of the Cooper pair for an arbitrarily weak attractive interaction between two electrons. This singularity is absent in the problem of three and few superconducting electrons at zero temperature on the full Fermi sea. Consequently, such three- and few-electron systems on the full Fermi sea do not form Cooper-type bound states for an arbitrarily weak attractive pair interaction., 10 pages. Accepted in European Physical Journal B

The elastic and inelastic scattering of ortho-positronium (Ps) by the hydrogen atom have been investigated using a three-Ps-state close-coupling approximation. The higher excitations and ionization of the Ps atom are treated within the framework of the Born approximation. In both cases the effect of electron exchange has been included by a parameter-free nonlocal model potential derived from an antisymmetrization of the wavefunction followed by the removal of nonorthogonality. Calculations are reported of scattering lengths, phase shifts, and of elastic, Ps excitation, and total cross sections. The trend of present target elastic total cross section agrees qualitatively with available experimental results on Ps-impact scattering.

Positronium (Ps) formation in positron-helium scattering has been investigated in different partial waves at medium energies including the Ore gap region using the close-coupling approximation with realistic wavefunctions for the following states: He(1s1s), He(1s2s), He(1s2p), He(1s3s), He(1s3p), Ps(1s), Ps(2s), Ps(2p). Calculations are reported of rearrangement cross sections to Ps(1s), Ps(2s) and Ps(2p) states for incident positron energies up to 200 eV. The present partial cross sections are in good agreement with experimental results and a variational calculation in the Ore gap region.

We study positron-helium scattering using close coupling approximation (CCA) employing different combinations of the following basis functions: He(1s1s), He(1s2s), He(1s2p), Ps(1s), and Ps(2s), where Ps stands for the positronium atom. We observe a prominent S wave resonance of width 2 eV at about 30 eV, in excitation and rearrangement cross sections to He(1s2s), He(1s2p), Ps(1s) and Ps(2s) states. We also report results of differential cross sections for the excitation of helium and positronium formation.

Made available in DSpace on 2022-04-28T19:54:34Z (GMT). No. of bitstreams: 0 Previous issue date: 1998-01-01 Positronium formation and target excitation in positron-helium scattering have been investigated using the close-coupling approximation with realistic wave functions for the positronium and helium atoms. The following eight states have been used in the close-coupling scheme: [Formula Presented] [Formula Presented] [Formula Presented] [Formula Presented] [Formula Presented] [Formula Presented] [Formula Presented] and [Formula Presented] where Ps stands for the positronium atom. Calculations are reported of differential cross sections for elastic scatering, inelastic target excitation to [Formula Presented] and [Formula Presented] states, and rearrangement transition to [Formula Presented] [Formula Presented] and [Formula Presented] states for incident positron energies between 40 and 200 eV. The coincidence parameters for the transition to the [Formula Presented] state of helium are also reported and briefly discussed. © 1998 The American Physical Society. Instituto de Física Teórica Universidade Estadual Paulista, São Paulo, 405-900 Instituto de Física Teórica Universidade Estadual Paulista, São Paulo, 405-900

The solutions of a renormalized BCS model are studied in two space dimensions for s, p and d waves for finite-range separable potentials. The gap parameter, the critical temperature , the coherence length and the jump in specific heat at as a function of the zero-temperature condensation energy exhibit universal scalings. In the weak-coupling limit, the present model yields a small and large , appropriate for high- cuprates. The specific heat, penetration depth and thermal conductivity as functions of temperature show universal scaling for p and d waves.

We demonstrate robust, stable, mobile excited states of quasi-two-dimensional (quasi-2D) dipolar Bose-Einstein condensate (BEC) solitons for repulsive contact interaction with a harmonic trap along the $x$ direction perpendicular to the polarization direction $z$. Such a soliton can freely move in the y-z plane. A rich variety of such excitations is considered: one quanta of excitation for movement along (i) y axis or (ii) z axis or (ii) both. A proposal for creating these excited solitonic states in a laboratory by phase imprinting is also discussed. We also consider excited states of quasi-2D dipolar BEC soliton where the sign of the dipolar interaction is reversed by a rotating orienting field. In this sign-changed case the soliton moves freely in the x-y plane under the action of a harmonic trap in the $z$ direction. At medium velocity the head-on collision of two such solitons is found to be quasi elastic with practically no deformation. The findings are illustrated using numerical simulation in three and two spatial dimensions employing realistic interaction parameters for a dipolar $^{164}$Dy BEC.

Made available in DSpace on 2018-12-11T16:56:37Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-10-20 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) We study a spin-orbit (SO)-coupled hyperfine spin-1 Bose-Einstein condensate (BEC) in a quasi-one-dimensional trap. For an SO-coupled BEC in a one-dimensional box, we show that in the absence of the Rabi term, any nonzero value of SO coupling will result in a phase separation among the components for a ferromagnetic BEC, like Rb87. On the other hand, SO coupling favors miscibility in a polar BEC, like Na23. In the presence of a harmonic trap, which favors miscibility, a ferromagnetic BEC phase separates, provided that the SO-coupling strength and number of atoms are greater than some critical value. The Rabi term favors miscibility irrespective of the nature of the spin interaction: ferromagnetic or polar. Instituto de Física Teórica, Universidade Estadual Paulista (UNESP) Instituto de Física Teórica, Universidade Estadual Paulista (UNESP) FAPESP: 2013/07213-0

An algebraic reformulation of the Bohr - Sommerfeld (BS) quantization rule is suggested and applied to the study of bound states in one-dimensional quantum wells. The energies obtained with the present quantization rule are compared to those obtained with the usual BS and WKB quantization rules and with the exact solution of the Schrodinger equation. We find that, in diverse cases of physical interest in molecular physics, the present quantization rule not only yields a good approximation to the exact solution of the Schrodinger equation, but yields more precise energies than those obtained with the usual BS and/or WKB quantization rules. Among the examples considered numerically are the Poeschl - Teller potential and several anharmonic oscillator potentials, which simulate molecular vibrational spectra and the problem of an isolated quantum well structure subject to an external electric field.

A narrow S-wave resonance has been found in the positron - helium system at about 30 eV, using the close-coupling approach, in excitation and rearrangement cross sections to He(1s2s), He(1s2p), Ps(1s) and Ps(2s) states by employing different combinations of the following basis functions: He(1s1s), He(1s2s), He(1s2p), Ps(1s) and Ps(2s), where Ps stands for the positronium atom.

We suggest a time-dependent mean-field hydrodynamic model for a binary dipolar boson-fermion mixture to study the stability and collapse of fermions in the ${}^{164}$Dy-${}^{161}$Dy mixture. The condition of stability of the dipolar mixture is illustrated in terms of phase diagrams. A collapse is induced in a disk-shaped stable binary mixture by jumping the interspecies contact interaction from repulsive to attractive by the Feshbach resonance technique. The subsequent dynamics is studied by solving the time-dependent mean-field model including three-body loss due to molecule formation in boson-fermion and boson-boson channels. Collapse and fragmentation in the fermions after subsequent explosions are illustrated. The anisotropic dipolar interaction leads to anisotropic fermionic density distribution during collapse. This study is carried out in three-dimensional space using realistic values of dipolar and contact interactions.

Trapped degenerate dipolar Bose and Fermi gases of the cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose–Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using a variational approximation and a numerical solution of a mean-field model. In the disc shape, with the polarization vector perpendicular to the plane of the disc, the atoms experience an overall dipolar repulsion and this fact should contribute to the stability. However, a complete numerical solution of the dynamics leads to the collapse of a strongly disc-shaped dipolar BEC due to the long-range anisotropic dipolar interaction. In the case of fermions, the stability of a trapped single-component degenerate dipolar Fermi gas is studied including the Hartree–Fock exchange and Brueckner–Goldstone correlation energies in the local-density approximation valid for a large number of atoms. Estimates for the maximum allowed number of polar Bose and Fermi molecules in the BEC and degenerate Fermi gas are given.

The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin in two and three space dimensions. This shows that lattice discretization technique could be a useful tool for the numerical solution of scattering problems in general. The approach is illustrated in the case of the Dirac delta function potential., 9 pages

We present results for medium-energy elastic, inelastic [transition to He(1s2 1 s), He(1s2 1 p), He(1s3 1 s), and He(1s3 1 p) states], capture [to Ps(1s), Ps(2s), and Ps(2p) states of the positronium (Ps) atom] and total cross sections of positron-helium scattering in the close coupling approach using realistic wave functions.

A parameter-free variational iterative method is proposed for scattering problems. The present method yields results that are far better, in convergence, stability and precision, than any other momentum space method. Accurate result is obtained for the atomic exponential (Yukawa) potential with an estimated error of less than 1 in 10 15 (10 10 ) after some 13 (10) iterations.

Made available in DSpace on 2022-04-28T19:53:30Z (GMT). No. of bitstreams: 0 Previous issue date: 1996-01-01 We present results for low- and medium-energy elastic and capture cross sections for positronium-atom–alkali-ion scattering using the coupled static close-coupling approximation. © 1996 The American Physical Society. Department of Theoretical Physics Indian Association for the Cultivation of Science, Calcutta, 700032 Instituto de Física Teórica Universidade Estadual Paulista, São Paulo, 01405 Instituto de Física Teórica Universidade Estadual Paulista, São Paulo, 01405

A complex system is often identified by the absence of a characteristic length, e.g. as in a fractal. A very large system subject to a fragmentation and/or aggregation dynamics passes through such complex configurations. We study statistically creation and maintenance of such configurations in space dimensions d=1 to 5 and find that they are easily created (maintained) for small (large) d. An intermediate d such as d=3 seems to be ideal for the creation and maintenance of complex systems. This has consequences in a statistical description of the universe.

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10 10 after some 8–10 iterations.

We present results for low-energy elastic S-, P-, and D-wave phase shifts, capture and total cross sections of positron-helium scattering with different basis sets in the close coupling approach using realistic wave functions for He(1s1s), He(1s21s), He(1s21p) and positronium (1s) states. A resonance is found in the S-wave capture cross section at 84 eV.

Complex Kohn variational principle is applied to the numerical solution of the fully off-shell Lippmann-Schwinger equation for nucleon-nucleon scattering for various partial waves including the coupled 3S1 -3D1 channel. Analytic expressions are obtained for all the integrals in the method for a suitable choice of expansion functions. Calculations with the partial waves 1S0 , 1P1, 1D2 , and 3S1 -3D1 of the Reid soft core potential show that the method converges faster than other solution schemes not only for the phase shift but also for the off-shell t matrix elements. We also show that it is trivial to modify this variational principle in order to make it suitable for bound-state calculation. The bound-state approach is illustrated for the 3S1 -3D1 channel of the Reid soft-core potential for calculating the deuteron binding, wave function, and the D state asymptotic parameters.