Related papers: KMS states on Quantum Grammars
The existence of a minimum measurable length scale was suggested by various theories of quantum gravity, string theory and black hole physics. Motivated by this, we examine a quantum theory exhibiting a minimum measurable time scale. We use…
To understand the dynamics of loop quantum gravity, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex. The…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
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. In this way, a physical clock with discrete…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical…
Quantum evolution of a two-spin system with anisotropic Heisenberg Hamiltonian in the magnetic field is considered. We show that this evolution happens on some manifold with geometry depending on the ratio between the interaction couplings…
We give a simple demonstration that the Schr\"odinger equation may be recast as a self-contained second-order Newtonian law for a congruence of spacetime trajectories. This provides a pictorial representation of the quantum state as the…
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…
Simulating large scale lattice dynamics directly is computationally demanding due to the high complexity involved, yet such simulations are crucial for understanding the mechanical and thermal properties of many physical systems. In this…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
One of the core questions of quantum physics is how to reconcile the unitary evolution of quantum states, which is information-preserving and time-reversible, with evolution following the second law of thermodynamics, which, in general, is…
It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…
We use spin coherent states to compare classical and quantum evolution of a simple paradigmatic, discrete-time quantum dynamical system exhibiting chaotic behavior in the classical limit. The spin coherent states are employed to define a…
A semiclassical theory of a quantum spin$-S$ model with competing ring and Heisenberg exchange terms on the triangular lattice is obtained. A mechanism for the generation of $Z_2$ vortices is exhibited. The vortices are shown to carry a…
Spin coherent states play a crucial role in defining QESM (quasi-exactly solvable models) establishing a strict correspondence between energy spectra of spin systems and low-lying quantum states for a particle moving in a potential field of…
The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same…
We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed…
General molecular dynamic approach, making possible direct calculation of eigen values and eigen functions for a quantum-mechanical system of an arbitrary symmetry is proposed. The method is based on analogy between discrete representation…