Related papers: Fermions from classical statistics
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
A homogeneous and isotropic cosmological model with a positive cosmological constant is considered. The matter sector is given by a massless scalar field, which can be used as an internal time to deparametrize the theory. The idea is to…
We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of…
The recently proposed probability representation of quantum mechanics is generalized to quantum field theory. We introduce a probability distribution functional for field configurations and find an evolution equation for such a…
We study numerically quantum diffusion of a particle on small-world networks by integrating the time-dependent Schr\"odinger equation with a localized initial state. The participation ratio, which corresponds to the number of visited sites…
We develop a dynamical framework for quantum measurement based on stochastic but unitary evolution in projective state space. Random Hamiltonians drawn from the Gaussian Unitary Ensemble generate stochastic unitary dynamics of the quantum…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
Quantum simulation is a rapidly evolving tool with great potential for research at the frontiers of physics, and is particularly suited to be used in computationally intensive lattice simulations, such as problems with non-equilibrium. In…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
An assessment is given as to the extent to which pure unitary evolution, as distinct from environmental decohering interaction, can provide the transition necessary for an observer to interpret perceived quantum dynamics as classical. This…
We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the…
In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
Glauber coherent states of quantum systems are reviewed. We construct the tomographic probability distributions of the oscillator states. The possibility to describe quantum states by tomographic probability distributions (tomograms) is…
Various classical counterparts for the two-level pairing model in a many-fermion system are presented in the Schwinger boson representation. It is shown that one of the key ingredients giving the classical descriptions for quantal system is…