相关论文: The quantum Neumann model: asymptotic analysis

We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…

For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of the universe as a sample point of an accumulative stochastic process. The model give predictions that are nearly identical…

In this talk we briefly review the concept of supersymmetric quantum mechanics using a model introduced by Witten. A quasi-classical path-integral evaluation for this model is performed, leading to a so-called supersymmetric quasi-classical…

We study the classical and quantum perturbation theory for two non--resonant oscillators coupled by a nonlinear quartic interaction. In particular we analyze the question of quantum corrections to the torus quantization of the classical…

Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…

In a metric variable based Hamiltonian quantization, we give a prescription for constructing semiclassical matter-geometry states for homogeneous and isotropic cosmological models. These "collective" states arise as infinite linear…

In this work we present (and encourage the use of) the Williamson theorem and its consequences in several contexts in physics. We demonstrate this theorem using only basic concepts of linear algebra and symplectic matrices. As an immediate…

We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…

Starting from the complete Mellin representation of Feynman amplitudes for noncommutative vulcanized scalar quantum field theory, introduced in a previous publication, we generalize to this theory the study of asymptotic behaviours under…

We review the main features of the relativistic Snyder model and its generalizations. We discuss the quantum field theory on this background using the standard formalism of noncommutaive QFT and discuss the possibility of obtaining a finite…

Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This gives a new solution of the the long standing problem of quantizing the resonances generically appearing…

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…

We formulate the error and disturbance in quantum measurement by invoking quantum estimation theory. The disturbance formulated here characterizes the non-unitary state change caused by the measurement. We prove that the product of the…

Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…

We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model, i.e. a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic…

The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the…

The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic…