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In a dissipationless linear lattice, spatial disorder or incommensurate modulation induce localization of the lattice eigenstates and block spreading of wave packets. Additionally, incommensurate arrays allow for the metal-insulator…
We propose a general approach to analyse diagonal ordering patterns in bosonic lattice models with algebraically decaying density-density interactions on arbitrary lattices. The key idea is a systematic search for the energetically best…
We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex-fluids,…
Au-Fe alloys are of immense interest due to their biocompatibility, anomalous hall conductivity, and applications in various medical treatment. However, irrespective of the method of preparation, they often exhibit a high-level of disorder,…
We consider one-dimensional asymmetric exclusion processes with a simple attractive interaction, where the distance between consecutive particles is not allowed to exceed a certain limit and investigate the consequences of this coupling on…
Using analytic and numerical methods, we study a $2d$ Hamiltonian model of interacting particles carrying ferro-magnetically coupled continuous spins which are also locally coupled to their own velocities. This model has been characterised…
We present a one-dimensional model for diffusion in a fluctuating lattice; that is a lattice which can be in two or more states. Transitions between the lattice states are induced by a combination of two processes: one periodic…
We investigate two-dimensional Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to an additional depletion of the superfluid density. We demonstrate…
We study many-body localization in a one dimensional optical lattice filled with bosons. The interaction between bosons is assumed to be random, which can be realized for atoms close to a microchip exposed to a spatially fluctuating…
Control of order-disorder phase transitions is a fundamental materials science challenge, underpinning the development of energy storage technologies such as solid oxide fuel cells and batteries, ultra-high temperature ceramics, and durable…
In this thesis, we develop analytical methods to study out-of-equilibrium stochastic processes driven by colored noise, i.e., noise with temporal correlations. These non-Markovian processes pose significant analytical challenges compared to…
In one-dimensional quantum emitter systems, the dynamics of atomic excitations are influenced by the collective coupling between emitters through photon-mediated dipole-dipole interactions. By introducing positional disorders in a portion…
We study the order-disorder transition in a collection of polar self-propelled particles, interacting through a distance dependent short range alignment interaction. A distance dependent interaction parameter $a_0$ is introduced such that…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I…
We study the effect of the boundary on a system of weakly interacting bosons in one dimension. It strongly influences the boson density which is completely suppressed at the boundary position. Away from it, the density is depleted over the…
In flat-band systems, destructive interference leads to the localization of non-interacting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighbouring single-particle…
We provide an account of the static and dynamic properties of hard-core bosons in a one-dimensional lattice subject to a multi-chromatic quasiperiodic potential for which the single-particle spectrum has mobility edges. We use the mapping…
Under an oscillating mechanical drive, an amorphous material progressively forgets its initial configuration and might eventually converge to a limit cycle. Beyond quasistatic drivings, how structurally disordered systems lose or record…
From the separability point of view the problem of two atoms interact with a single cavity mode is investigated. The density matrix is calculated and used to discuss the entanglement and to examine the dynamics of the local and non-local…