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Supersymmetry is a technique that allows us to extract information about the states and spectra of quantum mechanical systems which may otherwise be unsolvable. In this paper we reconstruct Ioffe's set of states for the singular…
In the context of count-in-cells statistics, the joint probability distribution of the density in two concentric spherical shells is predicted from first first principle for sigmas of the order of one. The agreement with simulation is found…
The quantized canonical space-time coordinates of a relativistic point particle are expressed in terms of the elements of a complex Clifford algebra which combines the complex properties of SL(2.C) and quantum mechanics. When the quantum…
In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…
We highlight the conceptual issues that arise when one applies the quasi-Hermitian framework to analyze scattering from localized non-Hermitian potentials, in particular complex square-wells or delta-functions. When treated in the framework…
Quantum subspace methods (QSMs) are a class of quantum computing algorithms where the time-independent Schrodinger equation for a quantum system is projected onto a subspace of the underlying Hilbert space. This projection transforms the…
In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in [Sasamoto-Wadati], [Barraquand-Corwin] and [Povolotsky] in the context of KPZ universality…
A pseudo-Hermitian coupled-channel square-well model is proposed, solved and discussed. The domain of parameters is determined where all the bound-state energies (twice degenerate with respect to the second observable which we call "spin")…
We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
The dissipation and decoherence (for example, the effects of noise in quantum computations), interaction with thermostat or in general with physical vacuum, measurement and many other complicated problems of open quantum systems are a…
Establishing a notion of the quantum state that applies consistently across space and time could be a crucial step toward formulating a relativistic quantum theory. We give an operational meaning to multipartite quantum states over…
Despite the astonishing successes of quantum mechanics, due to some fundamental problems such as the measurement problem and quantum arrival time problem, the predictions of the theory are in some cases not quite clear and unique.…
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,…
Statistical mechanical concepts and processes such as decoherence, correlation, and dissipation can prove to be of basic importance to understanding some fundamental issues of quantum cosmology and theoretical physics such as the choice of…
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…
Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…