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The calculation of the full counting statistics of the charge within a finite interval of an interacting one-dimensional system of electrons is a fundamental, yet as of now unresolved problem. Even in the non-interacting case, charge…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…
Starting from the Pauli Hamiltonian operator, we derive a scalar quantum kinetic equations for spin-1/2 systems. Here the regular Wigner two-state matrix is replaced by a scalar distribution function in extended phase space. Apart from…
Quantum-matter theory (QMT), based on the Schr\"odinger or Dirac equations, is firmly established for both intra- and intermolecular interactions. However, there are two key issues with QMT. First, its applicability to large molecular…
A central aim of physics is to describe the dynamics of physical systems. Schrodinger's equation does this for isolated quantum systems. Describing the time evolution of a quantum system that interacts with its environment, in its most…
In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schr\"odinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which…
Traditional derivations of the van der Waals equation typically use standard recipes involving ensemble averages of statistical mechanics. In this work, we study a box of weakly interacting gas particles in one-dimension from a purely…
Collisional reservoirs are becoming a major tool for modelling open quantum systems. In their simplest implementation, an external agent switches on, for a given time, the interaction between the system and a specimen from the reservoir.…
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…
To every product of $2\times2$ matrices, there corresponds a one-dimensional Schr\"{o}dinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors…
In classical mechanics matter and fields are completely separated. Matter interacts with fields. For particle physicists this is not the case. Both matter and fields are represented by particles. Fundamental interactions are mediated by…
The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double-scaling limit of the recursion relation…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
We study quantization of a self-interacting scalar field within the unfolded dynamics approach. To this end we find and analyze a classical unfolded system describing 4d off-shell scalar field with a general self-interaction potential. Then…
We show that the relation between the Schr\"odinger equation and diffusion processes has an algebraic nature and can be revealed via the structure of "duplex numbers." This helps one to clarify that quantum mechanics cannot be reduced to…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…