Related papers: Quantization of systems with temporally varying di…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
In curved spacetimes, the lack of criteria for the construction of a unique quantization is a fundamental problem undermining the significance of the predictions of quantum field theory. Inequivalent quantizations lead to different physics.…
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the…
Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
We study the emergence of statistical mechanics in isolated classical systems with local interactions and discrete phase spaces. We establish that thermalization in such systems does not require global ergodicity; instead, it arises from…
The Old Quantum Mechanics actions discretization rules for periodic motions on the atomic scale (Bohr-Sommerfeld) have been suitably modified in order to account the gravitational field instead of the electrostatic one. The new rules are…
A general canonical formalism for discrete systems is developed which can handle varying phase space dimensions and constraints. The central ingredient is Hamilton's principal function which generates canonical time evolution and ensures…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
The problem of time in canonical quantum gravity remains one of the most significant challenges, primarily due to the "frozen" formalism emerging from the Wheeler-DeWitt equation. Within the ADM formalism, we introduce a novel approach in…
Understanding the collective quantum dynamics of nonequilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum…
Collapse of the wave function appears to violate the quantum superposition principle as well as deterministic evolution. Objective collapse models propose a dynamical explanation for this phenomenon, by making a stochastic non-unitary and…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
Recent computer simulations reveal several intriguing features in the evolution of properties of amorphous solids subjected to repeated cyclic shear deformation. These include the divergence of the number of cycles to reach steady states as…
The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining…
In any dimension $D$, the Euclidean Einstein-Hilbert action, which describes gravity in the absence of matter, can be discretized over random discrete spaces obtained by gluing families of polytopes together in all possible ways. In the…
Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we…
The usual position-momentum commutation relation plays a fundamental role in the mathematical description of continuous-variable quantum systems. In the case of a qudit described by a Hilbert space of a high enough dimension, there exists a…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…