Related papers: Riemann hypothesis and Quantum Mechanics
The main topic of this paper is using Einstein's equivalence principle in the description of the gravity-induced wave function reduction in the framework of Bohmian causal quantum theory. However, such concept has been introduced and…
We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…
We present a new approach for obtaining quantum quasi-probability distributions, $P(\alpha,\beta)$, for two arbitrary operators, $\mathbf{a}$ and $\mathbf{b}$, where $\alpha$ and $\beta$ are the corresponding c-variables. We show that the…
A microscopic understanding of the thermodynamic entropy in quantum systems has been a mystery ever since the invention of quantum mechanics. In classical physics, this entropy is believed to be the logarithm of the volume of phase space…
The method of positive commutators, developed for zero temperature problems over the last twenty years, has been an essential tool in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive…
One of the principal objectives of quantum thermodynamics is to explore quantum effects and their potential beneficial role in thermodynamic tasks like work extraction or refrigeration. So far, even though several papers have already shown…
In this work we suggest a sufficiently simple for understanding "without knowing the details of the quantum gravity" and quite correct deduction of the Unruh temperature (but not whole Unruh radiation process!). Firstly, we shall directly…
We calculate the relaxation rate of a scalar field in a plasma of other scalars and fermions with gauge interactions using thermal quantum field theory. It yields the rate of cosmic reheating and thereby determines the temperature of the…
We consider $N$ i.i.d. Ising spins with mean $m\in (-1,1)$ whose interactions are described by a Sherrington-Kirkpatrick Hamiltonian with a quartic correction. This model was recently introduced by Bolthausen in \cite{Bolt2} as a toy model…
Number theory is an abstract mathematical field that has found a fertile environment for development in theoretical physics. In particular, several physical systems were related to the zeros of the Riemann-zeta function. In this work we…
We derive a system of TBA equations governing the exact WKB periods in one-dimensional Quantum Mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE/IM correspondence, and they can be regarded…
We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of the…
In the present study, we investigate the properties of an ensemble of free Dirac fermions, at finite inverse temperature $\beta$ and finite chemical potential $\mu$, undergoing rigid rotation with an imaginary angular velocity…
We explore Hilbert space reformulations of Riemann Hypothesis developed by Nyman, Beurling, B\'{a}ez-Duarte, et. al. with a weighted Bergman space $\mathcal{H}=A_1^2(\mathbb{D})$, i.e., Riemann hypothesis holds if and only if the Hilbert…
This work presents a unified perspective on thermal equilibrium and quantum dynamics by examining the simplest quantum system, a qubit, as a minimal model. We show that both the thermal partition function and the Loschmidt amplitude can be…
In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann Hypothesis. In the second part we review some physical problems related to this hypothesis: the links with Random Matrix…
By expressing the Schr\"odinger wave function in the form $\psi=Re^{iS/\hbar}$, where $R$ and $S$ are real functions, we have shown that the expectation value of $S$ is conserved. The amplitude of the wave ($R$) is found to satisfy the…
Established heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to…
We propose a novel method for renormalization group improvement of thermally resummed effective potential. In our method, $\beta$-functions are temperature dependent as a consequence of the divergence structure in resummed perturbation…
The thermodynamics and covariant kinetic theory have been elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis'…