相关论文: From ballistic motion to localization: a phase spa…

We demonstrate the existence of exact atypical many-body eigenstates in a class of disordered, interacting one-dimensional quantum systems that includes the Fermi-Hubbard model as a special case. These atypical eigenstates, which…

Localization of wavefunctions is arguably the most familiar effect of disorder in quantum systems. It has been recently argued [[V. Khemani, R. Nandkishore, and S. L. Sondhi, Nature Physics, 11, 560 (2015)] that, contrary to naive…

The two-dimensional hyperbolic plane, $\mathbb{H}^2$, is an unusual system in that dimensionality changes with scale: locally two-dimensional and planar at short distances, but effectively infinite-dimensional at large scales, it provides…

We consider a d-dimensional random quantum walk with site-dependent random coin operators. The corresponding transition coefficients are characterized by deterministic amplitudes times independent identically distributed site-dependent…

We present strong numerical evidence for the existence of a localization-delocalization transition in the eigenstates of the 1-D Anderson model with long-range hierarchical hopping. Hierarchical models are important because of the…

It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive…

We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…

The mean-field approach to two-site Bose-Hubbard systems is well established and leads to nonlinear classical equations of motion for the population imbalance and the phase difference. It can, e.g., be based on the representation of the…

Quantum phase transitions are usually observed in ground states of correlated systems. Remarkably, eigenstate phase transitions can also occur at finite energy density in disordered, isolated quantum systems. Such transitions fall outside…

It is assumed that the quantum state that may describe a macroscopic system at a given instant of time is one of the eigenstates of the reduced density matrix calculated from the wave function of the system plus its environment. This…

The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type…

An interpretation of the probability flux is given, based on a derivation of its eigenstates and relating them to coherent state projections on a quantum wavefunction. An extended definition of the flux operator is obtained using coherent…

Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the…

We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism…

We study the effect of local projective measurements on the quantum quench dynamics. As a concrete example, a one-dimensional Bose-Hubbard model is simulated by the matrix product state and time-evolving block decimation. We map out a…

We study the role played by noise on the QW introduced in [1], a 1D model that is inspired by a two particle interacting QW. The noise is introduced by a random change in the value of the phase during the evolution, from a constant…

Analytical complexity of quantum wavefunction whose argument is extended into the complex plane provides an important information about the potentiality of manifesting complex quantum dynamics such as time-irreversibility, dissipation and…

We examine the quantization of the motion of two charged vortices in a Ginzburg--Landau theory for the fractional quantum Hall effect recently proposed by the first two authors. The system has two second-class constraints which can be…

We introduce the mode connectivity as a measure of the number of eigenmodes of a wave equation connecting two points at a given frequency. Based on numerical simulations of scattering of electromagnetic waves in disordered media, we show…

The localization of a quantum state is numerically exhibited in a nonunitary Newtonian model for gravity. It is shown that an unlocalized state of a ball of mass just above the expected threshold of 10^11 proton masses evolves into a mixed…