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Several physical systems can be treated as a scattering process, and, for these processes, a natural observed quantity arises: the ratio between the reflected and incident intensities, known as the reflection coefficient. This dissertation…
A perturbative way to investigate superfluid properties of various systems under nonuniform potential is presented. We derive the perturbation expansion of the superfluid fraction, which indicates how liquid exhibits nonclassical rotational…
In one-dimensional diffusive processes with discrete steps characterized by geometrically decaying magnitudes, the usual Gaussian broadening familiar from Brownian motion is replaced by bounded probability distributions over particle…
Dynamics of classical scattering in the system of fermions is studied. The model is based on the coherent state representation and the equations of motion for fermions are derived from the time-dependent variational principle. It is found…
We study the defocusing energy-critical nonlinear wave equation in four dimensions. Our main result proves the stability of the scattering mechanism under random pertubations of the initial data. The random pertubation is defined through a…
Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…
We study the critical vortex shedding in a strongly interacting fermionic superfluid of $^{6}$Li across the BEC-BCS crossover. By moving an optical obstacle in the sample and directly imaging the vortices after time of flight, the critical…
In this work dark soliton collisions in a one-dimensional superfluid Fermi gas are studied across the BEC-BCS crossover by means of a recently developed finite-temperature effective field theory [S. N. Klimin, J. Tempere, G. Lombardi, J. T.…
We consider independent and $m$-dependent two-dimensional oriented site percolation with open-site density close to one started from Bernoulli product measures. We show that the probability of an occupied interval in the former process…
A quantum interference mechanism of the stripe phase instability in quasi one-dimensional (1D) repulsive electron system is proposed. The leading spin-charge coupling term in Landau functional is derived microscopically. It is shown that…
Small superconducting grains are discussed in the frameworks of both the reduced BCS Hamiltonian and the Universal Hamiltonian. It is shown that fluctuations of electrons in levels far from the Fermi energy dominate superconducting…
We consider a problem of superconductivity coexistence with the spin-density-wave order in disordered multiband metals. It is assumed that random variations of the disorder potential on short length scales render the interactions between…
We investigate the classical-quantum correspondence for particle motion in a superlattice in the form of a 2D channel with periodic modulated boundaries. Its classical dynamics undergoes the generic transition to chaos of Hamiltonian…
We study a model of spinless fermions with infinite nearest-neighbor repulsion on the square ladder which has microscopic supersymmetry. It has been conjectured that in the continuum the model is described by the superconformal minimal…
We study a model of spinless fermions on the honeycomb lattice with nearest-neighbor exclusion and extended repulsive interactions that exhibits `lattice supersymmetry' [P. Fendley, K. Schoutens, and J. de Boer, Phys. Rev. Lett. 90, 120402…
We investigate the problem of percolation of words in a random environment. To each vertex, we independently assign a letter $0$ or $1$ according to Bernoulli r.v.'s with parameter $p$. The environment is the resulting graph obtained from…
We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem…
We consider the Bernoulli Boolean discrete percolation model on the d-dimensional integer lattice. We study sufficient conditions on the distribution of the radii of balls placed at the points of a Bernoulli point process for the absence of…
Dense granular materials and other particle aggregates transmit stress in a manner that belies their microstructural disorder. A subset of the particle contact network is strikingly coherent, wherein contacts are aligned nearly linearly and…
For a general class of percolation models with long-range correlations on $\mathbb Z^d$, $d\geq 2$, introduced in arXiv:1212.2885, we establish regularity conditions of Barlow arXiv:math/0302004 that mesoscopic subballs of all large enough…