Related papers: Dephasing by a Continuous-Time Random Walk Process
Dynamical phase transitions in the relaxation behavior of stochastic quantum walks are investigated, focusing on systems where coherent unitary evolution is periodically interrupted by dephasing. This interplay leads to a classicalization…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
The fundamental assumption of dynamical decoupling based noise spectroscopy is that the coherence decay rate of qubit (or qubits) driven with a sequence of many pulses, is well approximated by the environmental noise spectrum spanned on…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
Elephant random walk is a kind of one-dimensional discrete-time random walk with infinite memory: For each step, with probability $\alpha$ the walker adopts one of his/her previous steps uniformly chosen at random, and otherwise he/she…
Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain…
This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…
We explore static noise in a discrete quantum random walk over a homogeneous cyclic graph, focusing on spectral and dynamical properties. Using a three-parameter unitary coin, we control the spectral structure of the noiseless step operator…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
We have investigated the time-evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can…
We address memory effects and diffusive properties of a continuous-time quantum walk on a one-dimensional percolation lattice affected by spatially correlated random telegraph noise. In particular, by introducing spatially correlated…
Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for noise spectroscopy are time-consuming, because they require measurements of the noise spectral…
We consider a quantized version of the Sinai-Derrida model for "random walk in random environment". The model is defined in terms of a Lindblad master equation. For a ring geometry (a chain with periodic boundary condition) it features a…
Quantum random walk finds application in efficient quantum algorithms as well as in quantum network theory. Here we study the mixing time of a discrete quantum walk over a square lattice in presence percolation and decoherence. We consider…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
We consider the complex branching random walk on a dyadic tree with Gaussian weights on the boundary between the diffuse phase and the glassy phase. We study the branching random walk in the space of continuous functions and establish…
A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion…
Quantum walks represent an excellent testbed for investigating the interplay between unitary coherent and incoherent dissipative processes. Thanks to photonic quantum interferometers of considerable size, experimental studies could be…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
The short-time behavior of quantum decay of an unstable state initially located within an interaction region of finite range is investigated using a resonant expansion of the survival amplitude. It is shown that in general the short-time…