Related papers: Reality from maximizing overlap in the periodic co…
Optimal (reversible) processes in thermodynamics can be modelled as step-by-step processes, where the system is successively thermalized with respect to different Hamiltonians by an external thermal bath. However, in practice interactions…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a generalized Hamiltonian dynamics in an extra time variable $\tau$ which, at…
Quantum superposition is often phrased as the ability to add state vectors. In practice, however, the physical quantity is a ray (a rank-one projector), so each input specifies only a projector and leaves a gauge freedom in the phases of…
The exploration of potential energy operators in quantum systems holds paramount significance, offering profound insights into atomic behaviour, defining interactions, and enabling precise prediction of molecular dynamics. By embracing the…
We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability…
We study the low temperature behaviour of path integrals for a simple one-dimensional model. Starting from the Feynman-Kac formula, we derive a new functional representation of the density matrix at finite temperature, in terms of the…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
Reinforcement Learning views the maximization of rewards and avoidance of punishments as central to explaining goal-directed behavior. However, over a life, organisms will need to learn about many different aspects of the world's structure:…
We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of…
Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The…
The control over quantum states in atomic systems has led to the most precise optical atomic clocks to date. Their sensitivity is currently bounded by the standard quantum limit, a fundamental floor set by quantum mechanics for uncorrelated…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
We argue that a basic modification must be made to the first quantised formalism of string theory if the physics of `particle creation' is to be correctly described. The analogous quantisation of the relativistic particle is performed, and…
We introduce a general framework for realizing $\mathcal{PT}$-like phase transitions in non-Hermitian systems without imposing explicit parity--time ($\mathcal{PT}$) symmetry. The approach is based on constructing a Hamiltonian as the…
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
We construct a one-particle TOA operator $\mathcal{\hat{T}}$ canonically conjugate with the Hamiltonian describing a free, charged, spin-$0$, relativistic particle in one spatial dimension and show that it is maximally symmetric. We solve…
The present study attempts to provide a consistent and coherent account of what the world could be like, given the conceptual framework and results of contemporary quantum theory. It is suggested that standard quantum mechanics can, and…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain)…