Related papers: A Gutzwiller trace formula for large hermitian mat…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
It has been argued that the existence of time crystals requires a spontaneous breakdown of the continuous time translation symmetry so to account for the unexpected non-stationary behavior of quantum observables in the ground state. Our…
We show, that the canonical invariant part of $\hbar$ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable…
In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schr\"odinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of…
We extend the It\^o-Wentzell formula for the evolution along a continuous semimartingale of a time-dependent stochastic field driven by a continuous semimartingale to tensor field-valued stochastic processes on manifolds. More concretely,…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…
We construct a qubit algebra from field creation and annihilation operators acting on a global vacuum state. Particles to be used as qubits are created from the vacuum by a near-deterministic single particle source. Our formulation makes…
Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
The differential structure of operator bases used in various forms of the Weyl-Wigner-Groenewold-Moyal (WWGM) quantization is analyzed and a derivative-based approach, alternative to the conventional integral-based one is developed. Thus…
Given a bipartite quantum system in an energy eigenstate, the dynamical description for one component can be derived via entanglement using the other component as a clock. This is the essence of the Page and Wootters mechanism. Moreover, if…
Simulation and analysis of multidimensional dynamics of a quantum non-Hmeritian system is a challenging problem. Gaussian wavepacket dynamics has proven to be an intuitive semiclassical approach to approximately solving the dynamics of…
We quantise and solve the dynamics of gravitational waves in a quantum Friedmann-Lemaitre-Robertson-Walker spacetime filled with perfect fluid. The classical model is formulated canonically. The Hamiltonian constraint is de-parametrised by…
A framework analogous to path integrals in quantum physics is set up for abstract dynamical systems in a W*-algebraic setting. We consider spaces of evolutions, defined in a specific way, of a W*-algebra A as an analogue of spaces of…
The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace…
This work introduces a quantum circuit synthesis framework for simulating the unitary time evolution under a subclass of symmetric Toeplitz Hamiltonians by decomposing them into specific diagonal matrices $M_k$. These matrices are then…
We have derived an analytical trace formula for the level density of the H\'enon-Heiles potential using the improved stationary phase method, based on extensions of Gutzwiller's semiclassical path integral approach. This trace formula has…
We propose a hybrid quantum-classical algorithm for the simulation of real-time dynamics in interacting quantum field theories coupled to classical fields, focusing on the self-consistent estimation of semiclassical backreaction. By…
The quantum baker's map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study…