Related papers: Do New Quantum Statistics Exist in Nature?
Quantum correlations can be naturally formulated in a classical statistical system of infinitely many degrees of freedom. This realizes the underlying non-commutative structure in a classical statistical setting. We argue that the quantum…
The classical and quantum dynamics of noncanonically coupled os- cillators is investigated in its relation to Lie superalgebras. It is shown that the quantum dynamics admits a hidden (super)hamiltonian formulation and, hence, preserves the…
Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry…
Quantum instruments are mathematical devices introduced to describe the conditional state change during a quantum process. They are completely positive map valued measures on measurable spaces. We may also view them as non-commutative…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
The phenomenon of universality is one of the most striking in many-body physics. Despite having sometimes wildly different microscopic constituents, systems can nonetheless behave in precisely the same way, with only the variable names…
A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory numbers statistics for the model of nonlinear dissipative oscillator. It is shown by numerical simulation of an ensemble of quantum trajectories…
We propose a very simple toy model of a $\mathbb{Z}_2^2$-supersymmetric quantum system and show, via Klein's construction, how to understand the system as being an $N=2$ supersymmetric system with an extra $\mathbb{Z}_2^2$-grading. That is,…
The upside-down simple harmonic oscillator system is studied in the contexts of quantum mechanics and classical statistical mechanics. It is shown that in order to study in a simple manner the creation and decay of a physical system by ways…
A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
A novel two-tiered organization of the microworld is presented, in which only the fundamental quantum fields of the standard model of particle physics (electrons, photons, quarks, etc.) are true quantum waves, exhibiting linear…
The classical boundaries of the quantum singular oscillator (SO) is addressed under Weyl-Wigner phase-space and Bohmian mechanics frameworks as to comparatively evaluate phase-space and configuration space quantum trajectories as well as to…
The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical…
Quantum theory revolutionised physics by introducing a new fundamental constant and a new mathematical framework to describe the observed phenomena at the atomic scale. These new concepts run counter to our familiar notions of classical…
We summarize basic features of quantum field theories with discrete symmetry $\mathbb{Q}/\mathbb{Z}$ (possibly higher form, global or gauged). The classification of representations and anomalies is quite rich and involves the ring of…
Quantum instruments derived from composite systems allow greater measurement precision than their classical counterparts due to coherences maintained between N components; spins, atoms or photons. Decoherence that plagues real-world devices…
Using a super-realization of the Wigner-Heisenberg algebra a new realization of the q-deformed Wigner oscillator is implemented.
Product states do not violate Bell inequalities. In this work, we investigate the quantumness of product states by violating a certain classical algebraic models. Thus even for product states, statistical predictions of quantum mechanics…