Related papers: Real-time dynamics from convex geometry
The paper proves that quantum mechanics is compatible with the constructive realism of modern philosophy of science. The proof is based on the observation that properties of quantum systems that are uniquely determined by their preparations…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…
The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non-Hermitian. Its imaginary part is the time…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
The simulation of quantum systems has been a key aim of quantum technologies for decades, and the generalisation to open systems is necessary to include physically realistic systems. We introduce an approach for quantum simulations of open…
The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
The accurate simulation of real--time quantum transport is notoriously difficult, requiring a consistent scheme to treat incoming and outgoing fluxes at the boundary of an open system. We demonstrate a method to converge non--equilibrium…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
Standard quantum mechanics predicts the non-conservation of state norms and probability when the fundamental requirement of the Hermiticity of the Hamiltonian is relaxed. Biorthogonal quantum mechanics, or the more general metric formalism,…
The simulation of quantum transport in a realistic, many-particle system is a nontrivial problem with no quantitatively satisfactory solution. While real-time propagation has the potential to overcome the shortcomings of conventional…
Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity.…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
We study a quantum theory with complex time parameter and non-Hermitian Hamiltonian structure. In this theory, the real part of the complex time is equal to `usual' physical time, whereas the imaginary one is proportional to inverse…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The…