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Inspired by works on the Anderson model on sparse graphs, we devise a method to analyze the localization properties of sparse systems that may be solved using cavity theory. We apply this method to study the properties of the eigenvectors…
This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…
We study the synchronization of $N$ nearest neighbors coupled oscillators in a ring. We derive an analytic form for the phase difference among neighboring oscillators which shows the dependency on the periodic boundary conditions. At…
The operation of autonomous finite-time quantum heat engines rely on the existence of a stable limit cycle in which the dynamics becomes periodic. The two main questions that naturally arise are therefore whether such a limit cycle will…
In isolated quantum many-body systems periodically driven in time, the asymptotic dynamics at late times can exhibit distinct behavior such as thermalization or dynamical freezing. Understanding the properties of and the convergence towards…
The collision terms in spin transport theory are analyzed in Kadanoff-Baym formalism for systems close to equilibrium. The non-equilibrium fluctuations in spin distribution include both damping and polarization, with the latter arising from…
An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The…
The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a…
Using a Krylov-subspace time evolution algorithm, we simulate the real-time dynamics of translation invariant non-integrable finite spin rings to quite long times with high accuracy. We systematically study the finite-size deviation between…
We investigate a two-dimensional superconducting system with a smoothly and periodically varying order parameter. The order parameter is modulated along one direction while remaining uniform in the perpendicular direction, leading to a…
In this thesis we give two applications of Ayoub's motivic nearby cycles functor: First we give a generalization of Grothendieck's classical local monodromy theorem. In the classical setup we show that the inertia group acts…
In the presence of a confining potential $V$, the eigenfunctions of a continuous Schr\"odinger operator $-\Delta +V$ decay exponentially with the rate governed by the part of $V$ which is above the corresponding eigenvalue; this can be…
In the hidden Markov process, there is a possibility that two different transition matrices for hidden and observed variables yield the same stochastic behavior for the observed variables. Since such two transition matrices cannot be…
It is shown that the infinite random Heisenberg XXZ spin-$\frac12$ chain exhibits localization phenomena, such as spectral, eigenstate, and weak dynamical localization, in an arbitrary (but fixed) energy interval in a non-trivial region of…
We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary…
Three eigenvalue bounds are derived for the instability of ideal compressible stratified magnetohydrodynamic shear flows in which the base velocity, density, and magnetic field vary in two directions. The first bound can be obtained by…
An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continu- ously coupled.…
Eigenvectors associated with non-degenerate eigenvalues are shown to correspond to columns of the adjugate of the characteristic matrix. Degenerate eigenvalues are associated with eigenvectors that correspond to reduced complement tensors…
A variance inequality for spin-flip systems is obtained using comparatively weaker knowledge of relaxation to equilibrium based on coupling estimates for single site disturbances. We obtain variance inequalities interpolating between the…
Asymptotically, we analytically derive the form of eigenvectors for two Fisher-Hartwig symbols besides those which were previously investigated in a $2016$ work due to Movassagh and Kadanoff, in which the authors characterized the…