Session B1: CM1: Condensed Matter

Bose-Einstein Condensate in solid helium

Neutron scattering measurements at high momentum and energy transfers, often referred to as deep inelastic neutron scattering (DINS), is the most effective tool to explore the dynamics of single particles in condensed matter. In liquid and solid helium for example, these measurements reveal the Bose-Einstein condensate (BEC) fraction and the average single-particle kinetic energy. In this talk, I will present recent DINS measurements of BEC in solid $^4$He at temperatures below the reported \lq supersolid' transition temperature of 200 mK. Within our current instrumental precision, we find that the BEC fraction, $n_0$, is consistent with zero.   

Molecular Production at a wide Feshbach resonance in Fermi-gas of cooled atoms

The problem of molecular production from degenerate gas of fermions at a wide Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction leads to significant renormalization of the gap between adiabatic levels. In contrast to static problem the close vicinity of exact resonance does not play substantial role. Two main physical results of our theory is the high sensitivity of molecular production to the initial value of magnetic field and generation of a large BCS condensate distributed over a broad range of momenta in inverse process of the molecule dissociation.   

Quantum Vortex Dynamics in two-dimensional neutral superfuids

We derive an effective action for the vortex translational zero modes of a superfluid by integrating out environmental modes which include phase and density fluctuations of the condensate. When the quantum dynamics of the fluctuations are treated as frozen with negligible Berry phases in adiabatic limit, we confirm the occurrence of vortex Magnus force and adiabatic vortex mass due to compressibility of the superfluids in agreement with earlier studies. We show that the adiabatic approximation is only valid in large system with small coherence length $R \gg \xi$. Furthermore, we also build a numerical model based on discrete Gross-Pitaevskii equation to show the renormalization and broadening of the vortex cyclotron resonance peaks. It is demonstrated that well-defined cyclotron peaks in spectral functions can be sustained only when the condition $R \gg \xi$ is satisfied. With the mapping between discrete Gross-Pitaevskii equation and bosonic single-band Hubbard model, we propose that the adiabatic vortex dynamics can be realized by tuning the ratio between tunneling energy $J$ and on-site interaction energy $U$ between atoms in cold atom systems with optical lattices such that $U \gg J$ .   

The Fourier-Bessel Method

Fourier split-step techniques are often used to compute soliton- like numerical solutions of the nonlinear Schrodinger equation. We discuss a new fourth-order implementation of the Fourier split-step algorithm for problems possessing azimuthal symmetry in 3+1-dimensions. This implementation is based, in part, on a finite difference approximation D=1/r d/dr 1/r that possesses an associated exact unitary representation of exp(i D) . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions [Nash2004]. Hence the attribute Fourier-Bessel for the method. The Fourier- Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed ``normal mode condensation.'' Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium.   

Continuous Neel to Bloch transition as thickness increases: statics and dynamics

This work studies the magnetic behavior of infinitely long ferromagnetic strips. Two different kinds of domain walls parallel to the long direction can occur in this system: Neel domain wall and Bloch domain wall. In very thin strips the Neel domain wall is energetically favorable. However, as the strips thickness increases, the energy of the Neel wall rapidly grows and at some critical thickness its exceeds the energy of the Bloch domain wall. The nature of this transition is not well understood. We analyze this system with the help of numerical and analytical methods. We found that it exhibits a type-II phase transition. The ground states on both sides of the transition are analyzed. For thicker samples, above the transition an asymmetric Bloch wall appears, in a 2nd order phase transition.   

Comparisons of Different Particle-Chain Methods for Path Integral Monte Carlo Methods

In previous work we have used Path Integral Monte Carlo methods to simulate a Positronium atom in a Lennard-Jones fluid. Trial positions are created for sub-chains of particles on the polymer chain to allow for proper exploration of the configuration space. Different methods can be used to determine how the different chains are selected. In this report we compare the results from simulations of Positronium in Xenon at 300 and 340K using our leap frog method and another method where the selection of the sub-chains for trial movements is done randomly. The results indicate that a random selection of sub-chains leads to more accurate simulation results at higher densities.   

Many-Body Density Matrix Perturbation Theory

One fundamental limitation of quantum chemical methods is the accuracy of the approximate many-body theoretical framework that is utilized. Accurate many-body formalisms for quantum chemical methods do exist, but these methods are computationally very expensive. Methods also exist that are much less computationally expensive such as Hatree-Fock, Density Functional and the Hybrid Functional theories, but at a reduced representation of the exact many-body ground state. This severely limits either the system size that can be addressed accurately, or the accuracy of the representation of the many-body ground state. What is essential is a method which represents the many-body ground state accurately, but with a low computational cost. Recently, a method for determining the response, to any order of the perturbation, within the density matrix formalism has been discovered. This method is very simple and computationally efficient, and it immediately opens up the possibility of computing the variational many-body ground state to unprecedented accuracy within a simplified computational approach. Within this article, we report on the theoretical development of this methodology, which we refer to as Many Body Density Matrix Perturbation Theory.   

Statistical Mechanical Proof of the Second Law of Thermodynamics based on Volume Entropy

As pointed out in [M. Campisi. Stud. Hist. Phil. M. P. 36 (2005) 275-290] the volume entropy (that is the logarithm of the volume of phase space enclosed by the constant energy hyper-surface) provides a good mechanical analogue of thermodynamic entropy because it satisfies the heat theorem and it is an adiabatic invariant. This property explains the ``equal'' sign in Clausius principle ($S_f \geq S_i$) in a purely mechanical way and suggests that the volume entropy might explain the ``larger than'' sign (i.e. the Law of Entropy Increase) if non adiabatic transformations were considered. Based on the principles of quantum mechanics here we prove that, provided the initial equilibrium satisfy the natural condition of decreasing ordering of probabilities, the expectation value of the volume entropy cannot decrease for arbitrary transformations performed by some external sources of work on a insulated system. This can be regarded as a rigorous quantum mechanical proof of the Second Law.