Related papers: Thoughts on Commutation Relations and Measurement …
We recommended consequent discrete combinatorial research in mathematical physics. Here we show an example how discretization of partial differential equations can be done and that quickly unexpected new findings can result from research in…
It is well-known that the coordinate as a continuous variable, consisting of a set of all points between 0 and $L$ contradicts the observability of measurement. In other words there might exist a fundamental length in nature, such as the…
The Dirac equation can be modelled as a quantum walk, with the quantum walk being: discrete in time and space (i.e. a unitary evolution of the wave-function of a particle on a lattice); homogeneous (i.e. translation-invariant and…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
The effect of measurement attributes (quantum level of precision, finite duration) on the classical and quantum correlations is analysed for a pair of qubits immersed in a common reservoir. We show that the quantum discord is enhanced as…
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for…
Recent experiments have demonstrated that measurements of the entropy change associated with the addition of electrons to semiconductor- and graphene-based quantum dots accurately quantify the spin and orbital degeneracy of the states into…
In a previous study it was demonstrated that Dirac's relativistic quantum equation for free electrons (DRQM)can be obtained from Maxwell's classical electromagnetic field equations (MaxEq). This raises fundamental issues about the…
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A new family of $2D$ walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac…
Using equations of motion with the anisotropic dissipative term for quantum particle and quantum-mechanical commutation rules, the general Maxwell-type differential equations are derived. The direct modifications of the well-known Maxwell…
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently…
A theoretical study is reported of electron transport at finite temperature in a double quantum dot (DQD) capacitively coupled to a quantum point contact (QPC). Starting from a Hamiltonian model, a master equation is obtained for the…
The usual position-momentum commutation relation plays a fundamental role in the mathematical description of continuous-variable quantum systems. In the case of a qudit described by a Hilbert space of a high enough dimension, there exists a…
Isometric fluctuation relations are deduced for the fluctuations of the order parameter in equilibrium systems of condensed-matter physics with broken discrete or continuous symmetries. These relations are similar to their analogues…
Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of…
We suggest commutation relations for a quantum measure. In one version of these relations, the right-hand side takes account of the presence of curvature of space; in the simplest case, this yields the action of general relativity. We…
As quantum optical phenomena are based on Maxwell's equations, and it is becoming important to understand quantum optical phenomena at short distances, so it is important to analyze quantum optics using short distance corrected Maxwell's…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations,…
A quantum thermodynamic system can conserve non-commuting observables, but the consequences of this phenomenon on relaxation are still not fully understood. We investigate this problem by leveraging an observable-dependent approach to…