Holstein model and Peierls instability in 1D boson-fermion lattice gases

We study an ultracold bose-fermi mixture in a one dimensional optical lattice. When boson atoms are heavier then fermion atoms the system is described by an adiabatic Holstein model, exhibiting a Peierls instability for commensurate fermion filling factors. A Bosonic density wave with a wavenumber of twice the Fermi wavenumber will appear in the quasi one-dimensional system.Comment: 5 pages, 4 figure

On the conversion efficiency of ultracold fermionic atoms to bosonic molecules via Feshbach resonances

We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of $^{40}$K and $^{6}$Li atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau Zener transition but faster than ``the collision rate'' in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficiency limit is due to the preparation of a statistical mixture of two spin-states, required to enable s-wave scattering. By constructing the many-body state of the system we show that this preparation yields a mixture of even and odd parity pair-states, where only even parity can produce molecules. The odd parity spin-symmetric states must decorrelate before the constituent atoms can further Feshbach scatter thereby increasing the conversion efficiency; ``the collision rate'' is the pair decorrelation rate.Comment: 4 pages, 3 figures, final version accepted to Phys. Rev. Let

Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction diffusion equations

Using spatial domain techniques developed by the authors and Myunghyun Oh in the context of parabolic conservation laws, we establish under a natural set of spectral stability conditions nonlinear asymptotic stability with decay at Gaussian rate of spatially periodic traveling-waves of systems of reaction diffusion equations. In the case that wave-speed is identically zero for all periodic solutions, we recover and slightly sharpen a well-known result of Schneider obtained by renormalization/Bloch transform techniques; by the same arguments, we are able to treat the open case of nonzero wave-speeds to which Schneider's renormalization techniques do not appear to appl

Many-body effects on adiabatic passage through Feshbach resonances

We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms Gamma on sweep rate alpha, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $Gamma\propto alpha$ is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law $Gamma\propto alpha^{1/3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.Comment: 9 pages, 9 figure

Nonlinear adiabatic passage from fermion atoms to boson molecules

We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction $\Gamma$ on the sweep rate $\alpha$ varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number $N$. The power-law is linear, $\Gamma \propto \alpha$, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and $\Gamma \propto \alpha^{1/3}$ when it is larger. Experimental data agree better with a linear dependence than with an exponential Landau-Zener fit, indicating that many-body effects are significant in the atom-molecule conversion process.Comment: 5 pages, 4 figure

Calculation of pure dephasing for excitons in quantum dots

Pure dephasing of an exciton in a small quantum dot by optical and acoustic phonons is calculated using the ``independent boson model''. Considering the case of zero temperature the dephasing is shown to be only partial which manifests itself in the polarization decaying to a finite value. Typical dephasing times can be assigned even though the spectra exhibits strongly non-Lorentzian line shapes. We show that the dephasing from LO phonon scattering, occurs on a much larger time scale than that of dephasing due to acoustic phonons which for low temperatures are also a more efficient dephasing mechanism. The typical dephasing time is shown to strongly depend on the quantum dot size whereas the electron phonon ``coupling strength'' and external electric fields tend mostly to effect the residual coherence. The relevance of the dephasing times for current quantum information processing implementation schemes in quantum dots is discussed

Spikes and diffusion waves in one-dimensional model of chemotaxis

We consider the one-dimensional initial value problem for the viscous transport equation with nonlocal velocity $u_t = u_{xx} - \left(u (K^\prime \ast u)\right)_{x}$ with a given kernel $K'\in L^1(\R)$. We show the existence of global-in-time nonnegative solutions and we study their large time asymptotics. Depending on $K'$, we obtain either linear diffusion waves ({\it i.e.}~the fundamental solution of the heat equation) or nonlinear diffusion waves (the fundamental solution of the viscous Burgers equation) in asymptotic expansions of solutions as $t\to\infty$. Moreover, for certain aggregation kernels, we show a concentration of solution on an initial time interval, which resemble a phenomenon of the spike creation, typical in chemotaxis models

Phonon-Coupled Electron Tunneling in Two and Three-Dimensional Tunneling Configurations

We treat a tunneling electron coupled to acoustical phonons through a realistic electron phonon interaction: deformation potential and piezoelectric, in two or three-dimensional tunneling configurations. Making use of slowness of the phonon system compared to electron tunneling, and using a Green function method for imaginary time, we are able to calculate the change in the transition probability due to the coupling to phonons. It is shown using standard renormalization procedure that, contrary to the one-dimensional case, second order perturbation theory is sufficient in order to treat the deformation potential coupling, which leads to a small correction to the transmission coefficient prefactor. In the case of piezoelectric coupling, which is found to be closely related to the piezoelectric polaron problem, vertex corrections need to be considered. Summing leading logarithmic terms, we show that the piezoelectric coupling leads to a significant change of the transmission coefficient.Comment: 17 pages, 4 figure

Well-Posedness for Semi-Relativistic Hartree Equations of Critical Type

We prove local and global well-posedness for semi-relativistic, nonlinear Schr\"odinger equations $i \partial_t u = \sqrt{-\Delta + m^2} u + F(u)$ with initial data in $H^s(\mathbb{R}^3)$, $s \geq 1/2$. Here $F(u)$ is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing $F(u)$, which arise in the quantum theory of boson stars, we derive a sufficient condition for global-in-time existence in terms of a solitary wave ground state. Our proof of well-posedness does not rely on Strichartz type estimates, and it enables us to add external potentials of a general class.Comment: 18 pages; replaced with revised version; remark and reference on blow up adde