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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…
We revisit pure quantum cosmology in three dimensions. The Wheeler-DeWitt equation can be solved perturbatively and the dynamics reduces to a particle on moduli space. Its time evolution is equivalent to the $T\overline{T}$ deformation.…
Coherence lengths of one particle states described by quantum wave functions are studied. We show that one particle states in various situations are not described by simple plane waves but are described by wave packets that are…
Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem…
Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical…
We consider time periodic Hamiltonian on periodic graphs and estimate the number of its quasi-energy eigenvalues on the finite interval.
Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of…
We study the classical and quantum mechanics of a free particle that collides elastically with the walls of a circular disk with the radius varying periodically in time. The quasi-energy spectral properties of the model are obtained from…
It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in…
We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on…
Turbulence is characterized by a large number of degrees of freedom, distributed over several length scales, that result into a disordered state of a fluid. The field of quantum turbulence deals with the manifestation of turbulence in…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…
With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions.…
We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit…
A calculation of the classical analogue for the quantum wave function and local denity of states, in energy representation, is presented for simple Hamiltonian systems. Sucha analogous were proposed by M. V. Berry and A. voros considering…
We study numerically the imperfection effects in the quantum computing of the kicked rotator model in the regime of quantum chaos. It is shown that there are two types of physical characteristics: for one of them the quantum computation…
The dynamics of a kicked quantum system undergoing repeated measurements of momentum is investigated. A diffusive behavior is obtained even when the dynamics of the classical counterpart is not chaotic. The diffusion coefficient is…