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Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of…
The Exact Foldy-Wouthuysen transformation (EFWT) method is generalized here. In principle, it is not possible to construct the EFWT to any Hamiltonian. The transformation conditions are the same but the involution operator has a new form.…
We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is…
In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite…
We demonstrate that complex point transformations can be used to construct non-Hermitian first integrals, time-dependent Dyson maps and metric operators for non-Hermitian quantum systems. Initially we identify a point transformation as a…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of…
State machines are a common model for robot behaviors. Transition functions often rely on parameterized conditions to model preconditions for the controllers, where the correct values of the parameters depend on factors relating to the…
Topological phase classifications have been intensively studied via machine-learning techniques where different forms of the training data are proposed in order to maximize the information extracted from the systems of interests. Due to the…
Quantum mechanical systems with position dependent masses (PDM) admitting for and more dimensional symmetry algebras are classified. Namely, all PDM systems are specified which, in addition to their invariance w.r.t. a three parametric Lie…
It is noted that the theory of neutrino oscillations can be constructed only in the framework of the particle physics theory, where is a mass shell conception and then transitions (oscillations) between neutrinos with equal masses are real…
Mixed quantum/classical theory (MQCT) for the treatment of rotationally inelastic transitions during collisions of two identical molecules, described either as indistinguishable or distinguishable partners, is reviewed. The treatment of two…
The Clausius-Clapeyron relation and its analogs in other first-order phase transitions, such as type-I superconductors, are derived using very elementary methods, without appealing to the more advanced concepts of entropy or Gibbs free…
We consider the general form of the linear transformation for point rotation coordinate frames. The frames have the rotation axis at every point. In the transformation the frequency of one frame relative to another is not equivalent to the…
A physical self-learning machine can be defined as a nonlinear dynamical system that can be trained on data (similar to artificial neural networks), but where the update of the internal degrees of freedom that serve as learnable parameters…
In this Paper we present an approach to Quantum Mechanical Canonical Transformations. Our main result is that Time Dependent Quantum Canonical Transformations can always be cast in the form of Squeezing Operators. We revise the main…
We study the minimal thermodynamically consistent model for an adaptive machine that transfers particles from a higher chemical potential reservoir to a lower one. This model describes essentials of the inhomogeneous catalysis. It is…
We consider a random two-phase process which we call a reset-return one. The particle starts its motion at the origin. The first, displacement, phase corresponds to a stochastic motion of a particle and is finished at a resetting event. The…
An important field in robotics is the optimization of controllers. Currently, robots are often treated as a black box in this optimization process, which is the reason why derivative-free optimization methods such as evolutionary algorithms…