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Weiping Zhang

Publications and source records attributed to Weiping Zhang.

At least 181 records · Page 10Linked to original sources
arXiv2007

Controllable Josephson-Like Tunneling in Two-Component Bose-Einstein Condensates Coupled with Microwave via Feshbach Resonance and Trapping Potential

We put forward a scheme for controlling Josephson-like tunneling in two-component Bose-Einstein condensates coupled with microwave field via Feshbach resonance and tuning aspect ratio of trapping potential. We prove how to realize a perfect periodic oscillation from a fast damped and irregular oscillation on relative number of atoms in future experiment. In particular, intensity of Josephson-like tunneling can be successfully controlled through controlling speed of recovering the initial value of intra-atomic interaction and aspect ratio of trapping potential. Interestingly, we find that relative number of atoms represents two different types of oscillation in respond to periodic modulation of attractive intra-atomic interaction.

cond-mat.other↗
arXiv2006

A Cheeger-Mueller theorem for symmetric bilinear torsions

We generalize a theorem of Bismut-Zhang, which extends the Cheeger-Mueller theorem on Ray-Singer torsion and Reidemeister torsion, to the case where the flat vector bundle over a closed manifold carries a nondegenerate symmetric bilinear form. As a consequence, we prove the Burghelea-Haller conjecture which gives an analytic interpretation of the Turaev torsion. It thus also provides an analytic interpretation of (not merely the absolute value of) the Alexander polynomial in knot theory.

math.DG↗
arXiv2006

Bergman kernels and symplectic reduction

We generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic identification property. More precisely, we study the asymptotic expansion of the $G$-invariant Bergman kernel of the spin^c Dirac operator associated with high tensor powers of a positive line bundle on a symplectic manifold. We also develop a way to compute the coefficients of the expansion, and compute the first few of them, especially, we obtain the scalar curvature of the reduction space from the $G$-invariant Bergman kernel on the total space. These results generalize the corresponding results in the non-equivariant setting, which has played a crucial role in the recent work of Donaldson on stability of projective manifolds, to the geometric quantization setting. As another kind of application, we generalize some Toeplitz operator type properties in semi-classical analysis to the framework of geometric quantization. The method we use is inspired by Local Index Theory, especially by the analytic localization techniques developed by Bismut and Lebeau.

math.DG↗
arXiv2006

Adiabatic Condition for Nonlinear Systems

We revisit the adiabatic criterion in stimulated Raman adiabatic passage for the three-level $Λ$-system, and compare the situation with and without nonlinearity. In linear systems, the adiabatic condition is derived with the help of the instantaneous eigenvalues and eigenstates of the Hamiltonian, a procedure that breaks down in the presence of nonlinearity. Using an explicit example relevant to photoassociation of atoms into diatomic molecules, we demonstrate that the proper way to derive the adiabatic condition for the nonlinear systems is through a linearization procedure.

quant-ph↗
arXiv2006

An Index Theorem for Toeplitz Operators on Odd Dimensional Manifolds with Boundary

We establish an index theorem for Toeplitz operators on odd dimensional spin manifolds with boundary. It may be thought of as an odd dimensional analogue of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. In particular, there occurs naturally an invariant of $η$ type associated to $K^1$ representatives on even dimensional manifolds, which should be of independent interests. For example, it gives an intrinsic interpretation of the so called Wess-Zumino term in the WZW theory in physics.

math.DG↗
arXiv2006

η-invariant and flat vector bundles II

We first apply the method and results in the previous paper to give a new proof of a result (hold in $ {\bf C}/{\bf Z}$) of Gilkey on the variation of h-invariants associated to non self-adjoint Dirac type operators. We then give an explicit local expression of certain h-invariant appearing in recent papers of Braverman-Kappeler on what they call refined analytic torsion, and propose an alternate formulation of their definition of the refined analytic torsion. A refinement in ${\bf C}$ of the above variation formula is also proposed.

math.DG↗
arXiv2005

Ultracold two-component Fermi gases with a magnetic field gradient near a Feshbach resonance

We study theoretically the ultracold two-component Fermi gases when a gradient magnetic field is used to tune the scattering length between atoms. For Li6 at the narrow resonance B0=543.25G, it is shown that the gases would be in a coexistence of the regimes of BCS, BEC and unitarity limit with the present experimental technique. In the case of thermal and chemical equilibrium, we investigate the density distribution of the gases and show that a double peak of the density distribution can give us a clear evidence for the coexistence of BCS, BEC and unitarity limit.

cond-mat.stat-mech↗
arXiv2005

$η$-invariant and flat vector bundles

We present an alternate definition of the mod {\bf Z} component of the Atiyah-Patodi-Singer $η$ invariant associated to (not necessary unitary) flat vector bundles, which identifies explicitly its real and imaginary parts. This is done by combining a deformation of flat connections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah, Patodi and Singer.

math.DG↗
arXiv2003

Inhibiting Three-Body Recombination in Atomic Bose-Einstein Condensates

We discuss the possibility of inhibiting three-body recombination in atomic Bose-Einstein condensates via the application of resonant $2π$ laser pulses. These pulses result in the periodic change in the phase of the molecular state by $π$, which leads to destructive interference between the decay amplitudes following successive pulses. We show that the decay rate can be reduced by several orders of magnitude under realistic conditions.

cond-mat.stat-mech↗
arXiv2003

Eta invariant and Chern-Simons current

We show that the R/Z part of the analytically defined eta invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, we discuss the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and prove an R refinement in the case where the Dirac operator is replaced by the Signature operator. We also extend the above discussion to the case of eta invariants associated to Hermitian vector bundles with non-unitary connection, which are constructed by using a trick due to Lott.

math.DG↗
arXiv2003

Circle actions and Z/k-manifolds

We establish an S^1-equivariant index theorem for Dirac operators on Z/k-manifolds. As an application, we generalize the Atiyah-Hirzebruch vanishing theorem for S^1-actions on closed spin manifolds to the case of Z/k-manifolds.

math.DG↗
arXiv2003

A Molecular Micromaser

We show that photoassociation of fermionic atoms into bosonic molecules inside an optical lattice can be described using a Jaynes-Cummings Hamiltonian with a nonlinear detuning. Using this equivalence to the Jaynes-Cummings dynamics, we show how one can construct a micromaser for the molecular field in each lattice site.

cond-mat.mes-hall↗
arXiv2003

Modular invariance, characteristic numbers and $η$ invariants

We generalize the "miraculous cancellation" formulas of Alvarez-Gaumé, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. We also apply our result to discuss intrinsic relations between the higher dimensional Rokhlin type congruence formulas of Ochanine [O1], Finashin [F] and Zhang [Z1, 2]. In particular, an analytic proof of the Finashin congruence formula is given.

math.DG↗
arXiv2003

Wave mixing of optical pulses and Bose-Einstein condensates

We investigate theoretically the four-wave mixing of optical and matter waves resulting from the scattering of a short light pulse off an atomic Bose-Einstein condensate, as recently demonstrated by D. Schneble {\em et al.} [ Science {\bf 300}, 475 (2003)]. We show that atomic ``pair production'' from the condensate results in the generation of both forward- and backward-propagating matter waves. These waves are characterized by different phase-matching conditions, resulting in different angular distributions and temporal evolutions.

cond-mat.soft↗
arXiv2003

Heat kernels and the index theorems on even and odd dimensional manifolds

In this talk, we review the heat kernel approach to the Atiyah-Singer index theorem for Dirac operators on closed manifolds, as well as the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. We also discuss the odd dimensional counterparts of the above results. In particular, we describe a joint result with Xianzhe Dai on an index theorem for Toeplitz operators on odd dimensional manifolds with boundary.

math.DG↗
arXiv2003

A fundamental limit for integrated atom optics with Bose-Einstein condensates

The dynamical response of an atomic Bose-Einstein condensate manipulated by an integrated atom optics device such as a microtrap or a microfabricated waveguide is studied. We show that when the miniaturization of the device enforces a sufficiently high condensate density, three-body interactions lead to a spatial modulational instability that results in a fundamental limit on the coherent manipulation of Bose-Einstein condensates.

cond-mat.stat-mech↗
arXiv2002

Feshbach-resonance-induced atomic filamentation and quantum pair correlation in atom-laser-beam propagation

We study the propagation of an atom laser beam through a spatial region with a magnetic field tuned to a Feshbach resonance. Tuning the magnetic field below the resonance produces an effective focusing Kerr medium that causes a modulational instability of the atomic beam. Under appropriate circumstances, this results in beam breakup and filamentation seeded by quasi-particle fluctuations, and in the generation of correlated atomic pairs.

cond-mat.mes-hall↗