Related papers: 2-D Covariant Affine Integral Quantization(s)
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum…
Covariant relativistic quantum theory is used to study the covariant Green's function, which can be used to determine the proper time evolved wave functions that are solutions to the covariant Schr\"odinger type equation for a massive spin…
Let $M$ be a smooth manifold equipped with a conformal structure, $E[w]$ the space of densities with the the conformal weight $w$ and $D_{w,w+\de}$ the space of differential operators from $E[w]$ to $E[w+\delta]$. Conformal quantization $Q$…
The correlated two-particle problem is solved analytically in the presence of a finite cavity. The method is demonstrated here in terms of exactly solvable models for both the cavity as well as the two-particle correlation where the…
In presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
Diffusion models are emerging models that generate images by iteratively denoising random Gaussian noise using deep neural networks. These models typically exhibit high computational and memory demands, necessitating effective post-training…
In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike…
An affine invariant point on the class of convex bodies in R^n, endowed with the Hausdorff metric, is a continuous map p which is invariant under one-to-one affine transformations A on R^n, that is, p(A(K))=A(p(K)). We define here the new…
Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…
Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented bounded in one orientation, e.g., a…
We show how to represent the state and the evolution of a quantum computer (or any system with an $N$--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary $N$, is…
Classical plane switching takes place in systems with a pronounced 1:2 resonance, where the degree of freedom with lowest frequency is doubly-degenerate. Under appropriate conditions, one observes a periodic and abrupt precession of the…
We show that real polarization method can be effectively used to geometrically quantize physical systems with compact phase space, like the spin. Our method enables us to construct a wave function of a qubit in both position and momentum…
For the continuous Wigner function and for certain discrete Wigner functions, permuting the values of the Wigner function in accordance with a symplectic linear transformation is equivalent to performing a certain unitary transformation on…
The negativity of a given state's Wigner function has been proposed as a measure of quantumness of that state in a unipartite system. This otherwise physically intuitive and useful phase-space measure however does not yield the right…
We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…
Granular systems confined in vertically vibrated shallow horizontal boxes (quasi two-dimensional geometry) present a liquid to solid phase transition when the frequency of the periodic forcing is increased. An effective model, where grains…
Quantisation with Gaussian type states offers certain advantages over other quantisation schemes, in particular, they can serve to regularise formally discontinuous classical functions leading to well defined quantum operators. In this work…