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We study the quantum theory of a simple general relativistic quantum model of two coupled harmonic oscillators and compute the two-point function following a proposal first introduced in the context of loop quantum gravity.
The Hamiltonian $H={1\over2} p^2+{1\over2}m^2x^2+gx^2(ix)^\delta$ with $\delta,g\geq0$ is non-Hermitian, but the energy levels are real and positive as a consequence of ${\cal PT}$ symmetry. The quantum mechanical theory described by $H$ is…
Derivation of two-time second-order correlation function by following approaches such as stochastic differential equation, coherent-state propagator, and quasi-statistical distribution function is presented. In the process, the time…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
A recently proposed generating functional allows the construction of the full set of n-point Green functions in QCD at high temperature and at distances larger than 1/gT. One may then learn how the system maintains its thermal equilibrium…
Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations…
Gaussian boson sampling is a promising scheme for demonstrating a quantum computational advantage using photonic states that are accessible in a laboratory and, thus, offer scalable sources of quantum light. In this contribution, we study…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…
We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by…
We analyze the non-Markovian dynamics of a quantum system subject to spontaneous collapse in space. After having proved, under suitable conditions, the separation of the center-of-mass and relative motions, we focus our analysis on the time…
An interpretation of non-relativistic quantum mechanics is presented in the spirit of Erwin Madelung's hydrodynamic formulation of QM and Louis de Broglie's and David Bohm's pilot wave models. The aims of the approach are as follows: 1) to…
The self-energy of the critical 3-dimensional O(N) model is calculated. The analysis is performed in the context of the Non-Perturbative Renormalization Group, by exploiting an approximation which takes into account contributions of an…
We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the…
Linear response functions are a cornerstone concept in physics as they enable efficient estimation of many dynamical properties. In addition to predicting dynamics of observables under perturbations without resimulating the system, these…
Reduction is shown to be a possible consequence of the basic principles of quantum mechanics, involving no branching of the quantum state of the universe. The key feature of a measurement is attributed to the creation of macroscopic germs…
We set up a general formalism for models of spontaneous wave function collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the…
Free-particle Green's function plays a central role in the theoretical description of electron scattering and autoionization processes in quantum physics and chemistry. Recently, Gaussian basis set approaches have become increasingly…
The problem of the initial conditions for the oscillator model of quantum dissipative systems is studied. It is argued that, even in the classical case, the hypothesis that the environment is in thermal equilibrium implies a statistical…
From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the…