Related papers: Phase-number uncertainty from Weyl commutation rel…
The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in…
It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that…
In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
Weyl's law approximates the number of states in a quantum system by partitioning the energetically accessible phase-space volume into Planck cells. Here we show that typical resonances in generic open quantum systems follow a modified,…
In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=exp[i phi] VU. Its most important application is to constrain how much a quantum state can be localised simultaneously in two…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
We present a survey on Weil sums in which an additive character of a finite field $F$ is applied to a binomial whose individual terms (monomials) become permutations of $F$ when regarded as functions. Then we indicate how these Weil sums…
We compute the phase diagram of strongly interacting fermions in one dimension at finite temperature, with mass and spin imbalance. By including the possibility of the existence of a spatially inhomogeneous ground state, we find regions…
Uncertainties $(\Delta x)^2$ and $(\Delta p)^2$ are analytically derived in an $N$-coupled harmonic oscillator system when spring and coupling constants are arbitrarily time-dependent and each oscillator is in an arbitrary excited state.…
We present some aspects of the fidelity approach to phase transitions based on lower and upper bounds on the fidelity susceptibility that are expressed in terms of thermodynamic quantities. Both commutative and non commutative cases are…
At high energy the standard model possesses conformal symmetry at the classical level. This is reflected at the quantum level by relations between the different beta functions of the model. These relations are known as the Weyl consistency…
Periodic orbit expressions for the density of states lead to spurious results when directly used to calculate quantities of thermodynamic interest. This is because the trace formula is usually valid only for large energies while the…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
Quantum phase transitions occur when quantum fluctuation destroys order at zero temperature. With an increase in temperature, normally the thermal fluctuation wipes out any signs of this transition. Here we identify a physical quantity that…
The liquid-gas phase transition and associated instability in two component systems are investigated using a mean field theory. The importance of the role of both the Coulomb force and symmetry energy terms are studied. The addition of the…
We define the notion of Weyl anomalies, measuring the violation of local scale invariance, in interacting quantum field theory on curved spacetimes in the framework of locally covariant field theory. We discuss some general properties of…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large…