The Thermodynamic Pressure of a Dilute Fermi Gas

We consider a gas of fermions with non-zero spin at temperature T and chemical potential μ. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as T is of the same order as the Fermi temperature, or smaller.     

Non-empirical pairing energy density functional

We perform systematic calculations of pairing gaps in semi-magic nuclei across the nuclear chart using the Energy Density Functional method and a non-empirical pairing functional derived, without further approximation, at lowest order in the two-nucleon vacuum interaction, including the Coulomb force. The correlated single-particle motion is accounted for by the SLy4 semi-empirical functional. Rather unexpectedly, both neutron and proton pairing gaps thus generated are systematically close to experimental data. Such a result further suggests that missing effects, i.e. higher partial waves of the NN interaction, the NNN interaction and the coupling to collective fluctuations, provide an overall contribution that is sub-leading as for generating pairing gaps in nuclei. We find that including the Coulomb interaction is essential as it reduces proton pairing gaps by up to 40%.     

Phase separation in the trapped spinor gases with anisotropic spin-spin interaction

We investigate the effect of the anisotropic spin-spin interaction on the ground state density distribution of the one dimensional spin-1 bosonic gases within a modified Gross-Pitaevskii theory both in the weakly interaction regime and in the Tonks-Girardeau (TG) regime. We find that for ferromagnetic spinor gas the phase separation occurs even for weak anisotropy of the spin-spin interaction, which becomes more and more obvious and the component of m_F=0 diminishes as the anisotropy increases. However, no phase separation is found for anti-ferromagnetic spinor gas in both regimes.     

Nonlinear wave interaction in photonic band gap materials

We present detailed analytical and numerical studies of nonlinear wave interaction processes in one-dimensional (1D) photonic band gap (PBG) materials with a Kerr nonlinearity. We demonstrate that some of these processes provide efficient mechanisms for dynamically controlling so-called gap-solitons. We derive analytical expressions that accurately determine the phase shifts experienced by nonlinear waves for a large class of non-resonant interaction processes. We also present comprehensive numerical studies of inelastic interactions, and show that rather distinct regimes of interaction exist. The predicted effects should be experimentally observable, and can be utilized for probing the existence and parameters of gap solitons. Our results are directly applicable to other nonlinear periodic structures such as Bose–Einstein condensates in optical lattices.     

A Total Measure of Multi-Particle Quantum Correlations in Atomic Schrödinger Cat States

We propose a total measure of multi-particle quantum correlation in a system of N two-level atoms (N qubits). We construct a parameter that encompasses all possible quantum correlations among N two-level atoms in arbitrary symmetric pure states and define its numerical value to be the total measure of the net atom-atom correlations. We use that parameter to quantify the total quantum correlations in atomic Schrödinger cat states, which are generated by the dispersive interaction in a cavity. We study the variation of the net amount of quantum correlation as we vary the number of atoms from N=2 to N=100 and obtain some interesting results. We also study the variation of the net correlation, for fixed interaction time, as we increase the number of atoms in the excited state of the initial system, and notice some interesting features. We also observe the behaviour of the net quantum correlation as we continuously increase the interaction time, for the general state of N two-level atoms in a dispersive cavity.     

The phase structure of Einstein–Cartan theory

In the Einstein–Cartan theory of torsion-free gravity coupling to massless fermions, the four-fermion interaction is induced and its strength is a function of the gravitational and gauge couplings, as well as the Immirzi parameter. We study the dynamics of the four-fermion interaction to determine whether effective bilinear terms of massive fermion fields are generated. Calculating one-particle-irreducible two-point functions of fermion fields, we identify three different phases and two critical points for phase transitions characterized by the strength of four-fermion interaction: (1) chiral symmetric phase for massive fermions in strong coupling regime; (2) chiral symmetric broken phase for massive fermions in intermediate coupling regime; (3) chiral symmetric phase for massless fermions in weak coupling regime. We discuss the scaling-invariant region for an effective theory of massive fermions coupled to torsion-free gravity in the low-energy limit.     

A coarse-grained model of the effective interaction for charged amino acid residues and its application to formation of GCN4-pLI tetramer

ABSTRACT

We present a simple coarse-grained model of the effective interaction for charged amino acid residues, such as Glu and Lys, in a water solvent. The free-energy profile as a function of the distance between two charged amino acid side-chain analogues in an explicit water solvent is calculated with all-atom molecular dynamics simulation and thermodynamic integration method. The calculated free-energy profile is applied to the coarse-grained potential of the effective interaction between two amino acid residues. The Langevin dynamics simulations with our coarse-grained potential are performed for association of a small protein complex, GCN4-pLI tetramer. The tetramer conformation reproduced by our coarse-grained model is similar to the X-ray crystallographic structure. We show that the effective interaction between charged amino acid residues stabilises association and orientation of protein complex. We also investigate the association pathways of GCN4-pLI tetramer.     

On the valence bond solid in the presence of Dzyaloshinskii-Moriya interaction

We examine the stability of the valence bond solid (VBS) phase against the Dzyaloshinskii-Moriya (DM) interaction in the bipartite lattice. We consider the VBS states in the AKLT model as well as the one in the Sandvik model in the 4×L lattice. We found that the VBS is very stable against the DM interaction qin the AKLT model. There is no quantum phase transition in the AKLT+DM case. However, the VBS spin gap closes in the Sandvik model due to the DM interaction.     

State transitions and the continuum limit for a 2D interacting, self-propelled particle system

We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the self-propulsion and interaction potential parameters. In this paper, we utilize a procedure which connects a class of individual-based models to their continuum formulations and determine criteria for the validity of the latter. H-stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions. We perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual-based one.     

Teleportation via a mixture of a two qubit subsystem of a N-qubit W and GHZ state

We study the thermal entanglement in the two-qubit Heisenberg XXZ model with the Dzyaloshinskii-Moriya (DM) interaction, and teleport an unknown state using the model in thermal equilibrium state as a quantum channel. The effects of DM interaction, including D_x and D_z interaction, the anisotropy and temperature on the entanglement and fully entangled fraction are considered. What deserves mentioning here is that for the antiferromagnetic case, the D_x interaction can be more helpful for increasing the entanglement and critical temperature than D_z, but this cannot for teleportation.     

Role of allowance for interaction of distant neighbors in loss of stability in an extended anharmonic atomic chain

We investigate the problem of loss of stability in an anharmonic atomic chain whose ends are subject to a constant tensile stress when we allow for interaction of not only immediate neighbors, but distant neighbors as well. Using the approximation of self-consistent phonons, we obtain general expressions for the law of dispersion for natural oscillations of the chain and the equilibrium interatomic distance. We perform a concrete analysis for the pairwise interatomic Morse potential. Together with the case of first and second neighbors, we consider the general case of interaction of all atoms with each other. We show that instability appears simultaneously in all oscillation modes. Allowance for the interaction of more distant neighbors as well as closer neighbors increases the domain of stability of a chain relative to external stresses. V. I. Lenin Moscow State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 103–108, May, 1997.     

Quantum Mechanics of Two-Field Parametric Frequency Converter Interacting with a Single Atom

In this communication we deal with a new model Hamiltonian representing the interaction between a two-level atom and two electromagnetic field modes in a cavity. The interaction between the modes has been taken into account and considered to be of a parametric frequency converter type. The model can be regarded as a generalization of two different systems: the Jaynes–Cummings model (atom–field interaction) and the two-mode frequency converter model (field–field interaction). Under a certain condition an exact solution for the equations of motion in the Heisenberg picture is given. The wavefunction in the Schrödinger picture is also constructed and used to discuss some statistical properties related to the model. We assume that the fields are initially in coherent states. We discuss atomic inversion, photon number distribution, squeezing and other phenomena. We show in all cases that the system is very sensitive to any variation in the mean photon numbers.     

Polaronic aspects of spin polarized hydrogen of films of liquid He

We have studied the interaction of a collection of 2-D spin polarized hydrogen (H↓) atoms with the ripplon modes of a superfluid liquid helium film. From the deformation correction to the effective H↓He potential we derive the H↓-ripplon interaction Hamiltonian. We find that a weak coupling polaron state can form and we make specific predictions for the change in H↓ energy and effective mass which arise as a consequence. We also make a direct comparison (in coordinate space) of the ripplon mediated ↓-H↓ interaction, V_R(r), with the usual H↓H↓ interaction V(r).     

Competing polarization mechanisms in the heavy-fermion paramagnet CeCu<Subscript><Emphasis Type="Bold">6</Emphasis></Subscript>

Nuclear magnetic resonance (NMR) and relaxation of ⁶³Cu and ⁶⁵Cu in a powder sample of the heavy-fermion paramagnet CeCu₆ is measured and analysed quantitatively. Five different Cu sites are accessible to a detailed analysis. We derive quadrupolar splitting frequencies, Ce to Cu transferred hyperfine field coupling constants, and transversal as well as longitudinal relaxation behaviour. Only small relaxation anomalies are observed at the orthorhombic to monoclinic structural phase transition of CeCu₆. We point to the different importance of transferred hyperfine interaction and local conduction electron density for static or dynamic part, respectively, of Cu hyperfine interaction. The different sign of the transferred hyperfine interaction from Ce³⁺ to different Cu neighbours reveals the different competing interaction mechanisms, giving rise to the heavy-fermion paramagnetic behavior of CeCu₆. Received 20 November 2001     

Energy localization and transport in two-dimensional Fermi–Pasta–Ulam lattices

We investigate energy localization and transport in the form of discrete breathers and their movability in two-dimensional Fermi–Pasta–Ulam(FPU) lattices. We study the dynamics of the two-dimensional Fermi–Pasta–Ulam(FPU) lattice, incorporating the complicated effects of geometry, long-range interactions as well as nonlinear dispersion. We obtain several exact discrete breather(DB) solutions, such as the odd-parity and even-parity DBs, compact-like DBs and moving DBs for various geometries of the two-dimensional FPU chain. We show that DBs also exist in the same lattice in presence of next-nearest neighbour interaction. Large-amplitude exact subsonic travelling kink-soliton solutions are obtained in such a periodic chain in presence of long-range nonlinear dispersive interaction in the long-wavelength and weakly nonlinear limit. Such a two-dimensional FPU lattice admits finite amplitude nonlinear sinusoidal wave (NSW) solutions with short commensurate as well as incommensurate wavelengths for different geometries of the chain. The usefulness of these solutions for energy localization and transport in various physical systems are discussed.     

The boundary element approach to Van der Waals interactions

We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response of a general boundary shape. We achieve this by rewriting the interaction energy expression presented in Phys. Rev. B, 62 (2000) 6997 exclusively in terms of surface integrals of surface operators. We validate this approach in the Lifshitz case and give numerical results for the interaction of two spheres as well as the van der Waals self-interaction of a uniaxial ellipsoid. Our method is simple to implement and is particularly suitable for a full, non-perturbative numerical evaluation of non-retarded van der Waals interactions between objects of a completely general shape.     

Effects of three-body interactions in the parametric and modulational instabilities of Bose-Einstein condensates

The parametric modulational instability for a discrete nonlinear Schrödinger equation with a cubic-quintic nonlinearity is analyzed. This model describes the dynamics of BECs, with both two- and three-body interatomic interactions trapped in an optical lattice. We identify and discuss the salient features of the three-body interaction in the parametric modulational instability. It is shown that the three-body interaction term can both, shift as well as narrow the window of parametric instability, and also change the behavior of a modulationally stable and parametrically unstable BEC with attractive two-body interaction. We explore this instability through the multiple-scale analysis and identify it numerically. The effect of the three body losses have also been investigated.