Related papers: Time evolution in deparametrized models of loop qu…
The slow-roll approximation is an analytical approach to study dynamical properties of the inflationary universe. In this article, systematic construction of the slow-roll expansion for effective loop quantum cosmology is presented. The…
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…
The techniques employed to solve the interaction of a detector and a quantum field typically require perturbation methods. We introduce mathematical techniques to solve the time evolution of an arbitrary number of detectors interacting with…
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman and von Neumann and was developed in later decades by many…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time-dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian…
We formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (\partial_t^2+D)\psi(t)=0, where D is a positive-definite operator acting in a Hilbert space \tilde H. We determine all the positive-definite inner…
We present the method of describing an evolution in quantum cosmology in the framework of the reduced phase space quantization of loop cosmology. We apply our method to the flat Friedman-Robertson-Walker model coupled to a massless scalar…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series…
I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper…
One of the standard approaches of incorporating the quantum gravity (QG) effects into the semiclassical analysis is to adopt the notion of a quantum-corrected spacetime arising from the QG model. This procedure assumes that the expectation…
The Hamiltonian approach to General Relativity is developed similarly to the Wheeler-DeWitt Hamiltonian cosmology, where the cosmological scale factor is treated as a time-like dynamic variable and its canonical momentum is considered as an…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian…
Phenomenological studies of quantum gravity have proposed a modification of the commutator between position and momentum in quantum mechanics so to introduce a minimal uncertainty in position in quantum mechanics. Such a minimal uncertainty…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by…
We perform a canonical, reduced phase space quantisation of General Relativity by Loop Quantum Gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the combination of 1. the Brown -- Kuchar…