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We review here the development of the general formalism for the study of fermion propagation in the presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival…
We analyze the decoherence dynamics of a central spin coupled to a spin chain with a time-dependent noisy magnetic field, focusing on how noise influences the system's decoherence. Our results show that decoherence due to the nonequilibrium…
We extend a perturbative Dyson-type treatment and discrete-symmetry constraints from the Schr\"{o}dinger and von Neumann equations to a dephasing Lindblad framework. This work develops further the odd-symmetric formulation involving dual…
Collective synchronization is often summarized by a complex order parameter $R e^{i\Psi}$, implicitly treating the global phase $\Psi$ as a meaningful macroscopic coordinate. Here we ask when $\Psi$ becomes \emph{operationally well-defined}…
We study a series of $N$ oscillators each coupled to its nearest neighbours, and linearly to a phonon field through the oscillator's number operator. We show that the Hamiltonian of a pair of adjacent oscillators, or a dimer, within the…
We consider the symmetric single-impurity Anderson model in the presence of pairing fluctuations. In the isotropic limit, the degrees of freedom of the local impurity are separated into hybridizing and non-hybridizing modes. The self-energy…
Extraneous motion of optical elements in an interferometer lead to excess noise. Typically, fluctuations in the effective path length lead to phase noise, while beam-pointing leads to apparent amplitude noise. For a transmissive optic…
The particles produced from the vacuum in the dynamical Casimir effect are highly entangled. In order to quantify the correlations generated by the process of vacuum decay induced by moving mirrors, we study the entanglement evolution in…
Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as…
Phase insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state [1 - 5]. However, this fundamental noise penalty in amplification can be…
We numerically study the effect of adding quenched disorder in the form of randomly placed pinning sites on jamming transitions in systems that jam at a well defined point J in the clean limit. Quenched disorder decreases the jamming…
We study analytically and numerically the problem of a nonlinear mechanical oscillator with additive noise in the absence of damping. We show that the amplitude, the velocity and the energy of the oscillator grow algebraically with time.…
The onset of undamped wave propagation in noisy self-oscillatory media is identified with a Hopf bifurcation of the corresponding effective dynamical system obtained by properly renormalizing the effects of noise. We illustrate this fact on…
We consider non-Hermitian tight-binding one-dimensional Hamiltonians and show that imposing a certain symmetry causes all eigenvalues to pair up and the corresponding eigenstates to coalesce in pairs. This Pairwise Coalescence (PC) is an…
A general master equation is derived to describe an electromechanical single-dot transistor in the Coulomb blockade regime. In the equation, Fermi distribution functions in the two leads are taken into account, which allows one to study the…
The possibility of charge density oscillations in a {\it finite-thickness} two-dimensional system is investigated for strong magnetic fields and integer filling factors. Using an effective action formalism, it is shown that an {\it…
There has been considerable effort expended towards understanding high temperature superconductors (HTSC), and more specifically the cuprate phase diagram as a function of doping level. Yet, the only agreement seems to be that HTSC is an…
Casimir friction is analyzed for a pair of dielectric particles in relative motion. We first adopt a microscopic model for harmonically oscillating particles at finite temperature T moving non-relativistically with constant velocity. We use…
We study an $O(N)$ invariant surface defect in the Wilson-Fisher conformal field theory (CFT) in $d=4-\epsilon$ dimensions. This defect is defined by mass deformation on a two-dimensional surface that generates localized disorder and is…
We formally extend the CFT techniques introduced in arXiv:1505.00963, to $\phi^{\frac{2d_0}{d_0-2}}$ theory in $d=d_0-\epsilon$ dimensions and use it to compute anomalous dimensions near $d_0=3, 4$ in a unified manner. We also do a similar…