Related papers: Time Evolution of Typical Pure States from a Macro…
We consider an isolated macroscopic quantum system in a pure state $\psi_t$ evolving unitarily in a separable Hilbert space $\mathcal{H}$ and take for granted that different macro states $\nu$ correspond to mutually orthogonal subspaces…
We consider a closed macroscopic quantum system in a pure state $\psi_t$ evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces $\mathcal{H}_\nu$ (macro spaces) of Hilbert space, each…
Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator $\rho$ of low purity, $\tr\rho^2\ll 1$, and yielding the ensemble averaged expectation value $\tr(\rho A)$ for any…
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…
For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrodinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann's…
We study the time evolution of superposition of product states of two dressed atoms in a spherical cavity in the extreme situations of an arbitrarily large cavity (free space) and of a small one. In the large-cavity case, the system…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
The nodes are traditionally viewed as fixed points where the probability density vanishes. However, this work demonstrates that these nodes exhibit time-dependent oscillation in quantum superposition states. We derive this effect for a…
We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
Time evolution of macroscopic systems is re-examined primarily through further analysis and extension of the equation of motion for the density matrix $\rho(t)$. Because $\rho$ contains both classical and quantum-mechanical probabilities it…
We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary…
Motivated by describing time-evolutions of noncommutative worlds, I discuss symmetry-preserving evolutions of noncommutative worlds of finite dimensional representation spaces. An interesting issue in such evolutions is that there can be…
An infinite system of point particles performing random jumps in $\mathds{R}^d$ with repulsion is studied. The states of the system are probability measures on the space of particle's configurations. The result of the paper is the…
We consider a free fermion chain with uniform nearest-neighbor hopping and let it evolve from an arbitrary initial state with a fixed macroscopic number of particles. We then prove that, at a sufficiently large and typical time, the…
In the formulation of Banks, Peskin and Susskind, we show that one can construct evolution equations for the quantum mechanical density matrix $\rho$ with operators which do not commute with hamiltonian which evolve pure states into mixed…
Dynamical evolution of the quantum ground state (vacuum) is analyzed for time variant harmonic oscillators characterized by asymptotically constant frequency. The oscillatory density matrix in the asymptotic future is uniquely determined by…
For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum…
The unitarity of quantum evolutions implies that the overlap between two initial states does not change in time. This property is commonly believed to explain the lack of state sensitivity in quantum theory, a feature that is prevailing in…