Related papers: Anharmonic quantum mechanical systems do not featu…
A complete theoretical treatment in many problems relevant to physics, chemistry, and biology requires considering the action of the environment over the system of interest. Usually the environment involves a relatively large number of…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
It is commonly stated that decoherence in open quantum systems is due to growing entanglement with an environment. In practice, however, surprisingly often decoherence may equally well be described by random unitary dynamics without…
On the example of a quantum oscillator the connection of the dynamical coherent state with the phase symmetry breaking and the existence of the nondissipative motion is considered. In multiparticle systems of interacting particles similar…
The driven quantum harmonic oscillator is fundamental to a number of important physical systems. Here, we consider the quantum harmonic oscillator under non-Hermitian, PT-symmetric driving, showing that the resulting set of Wigner-space…
Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
Trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations are shown to be classical trajectories. Under convenient conditions, they may exhibit properties typical of chaotic behavior in…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
We discuss here phase transitions in quantum field theory in the context of vacuum realignment through an explicit construction. Vacuum destabilisation may occur through a scalar attaining a nonzero expectation value, or through a…
There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current~$\bf J$. This current reveals fine details of quantum dynamics -- finer than is…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
The behaviour of classical mechanical systems is characterised by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why…
A nonequilibrium statistical operator method is developed for ensembles of particles obeying non-Hamiltonian equations of motion in classical phase space. The main consequences of non-zero compressibility of phase space are examined in…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…