Related papers: Random walk on quantum blobs
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
Interesting non-linear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator valued distributions. Therefore, one is usually forced to find a…
We investigate the properties of a quantum walk which can simulate the behavior of a spin $1/2$ particle in a model with an ordinary spatial dimension, and one extra dimension with warped geometry between two branes. Such a setup…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplectic Howe condition, we show that there is a canonical…
Quantum walks constitute a rich area of quantum information science, where multipartite entanglement plays a central role in the dynamics and scalability of quantum advantage over classical simulators. In this work, we study the…
We consider quantum graphs with spin-orbit couplings at the vertices. Time-reversal invariance implies that the bond S-matrix is in the orthogonal or symplectic symmetry class, depending on spin quantum number s being integer or…
Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…
A variational phase space is constructed for a compact and piecewise flat Riemannian manifold. An extended action functional is provided such that the variational dynamics generate a symplectic flow on the phase space. This symplectic flow…
We present a general framework for reduction of symplectic Q-manifolds via graded group actions. In this framework, the homological structure on the acting group is a multiplicative multivector field.
We introduce a new kind of groupoid--a pseudo \'etale groupoid, which provides many interesting examples of noncommutative Poisson algebras as defined by Block, Getzler, and Xu. Following the idea that symplectic and Poisson geometries are…
We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols,…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space-time by means of a generalized microcanonical ensemble similar to the one of the standard…
In this work we review, complete, and synthesize results linking generalized coherent stages (nondegradable Gaussian wavefunctions) to the notions of Fermi ellipsoids, quantum blobs, and microlocal pairs introduced in previous work. These…
In this paper, we show the relation between $sp(4,\mathbb{R})$, the Lie algebra of the symplectic group, and the elements of $Sp(4,\mathbb{R})$. We use this result to obtain some special cases of symplectic matrices relevant to the study of…
We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.
In this doctoral thesis we have studied the quantum properties of several models which have been classified as statical and dynamical systems. The first part has been devoted to investigate the properties of the statical models including…
We propose a general framework for quantum walks on d-dimensional spaces. We investigate asymptotic behavior of these walks. Among them, existence of limit distribution of homogeneous walks is proved. In this theorem, the support of the…
We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by…