Related papers: On the measure division construction of \Lambda-co…
The study of topological bandstructures is an active area of research in condensed matter physics and beyond. Here, we combine recent progress in this field with developments in machine-learning, another rising topic of interest.…
An exactly solvable model for a quantum measurement is discussed which is governed by hamiltonian quantum dynamics. The $z$-component $\hat s_z$ of a spin-1/2 is measured with an apparatus, which itself consists of magnet coupled to a bath.…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
The way Quantum Mechanics (QM) is introduced to people used to Classical Mechanics (CM) is by a complete change of the general methodology) despite QM historically stemming from CM as a means to explain experimental results. Therefore, it…
In this paper we construct general vector-valued infinite-divisible independently scattered random measures with values in $\mathbb{R}^m$ and their corresponding stochastic integrals. Moreover, given such a random measure, the class of all…
Wavefunction collapse is commonly associated with unavoidable physical disturbance of the measured system. Here we show that in driven-dissipative quantum systems, continuous measurement can induce strong trajectory-level collapse while…
This paper defines two decreasing measures for terms of the simply typed lambda-calculus, called the W-measure and the Tm-measure. A decreasing measure is a function that maps each typable lambda-term to an element of a well-founded…
Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism $f\in\Diff(M)$. We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages…
Type A N-fold supersymmetry of one-dimensional quantum mechanics can be constructed by using sl(2) generators represented on a finite dimensional functional space. Using this sl(2) formalism we show a general method of constructing Type A…
A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…
Wilson lines, being comparators that render non-local operator products gauge invariant, are extensively used in QCD calculations, especially in small-$x$ calculations, calculations concerning validation of factorisation schemes and in…
We consider shock measures in a class of conserving stochastic particle systems on Z. These shock measures have a product structure with a step-like density profile and include a second class particle at the shock position. We show for the…
Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalising and improving upon the…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
We show how distinct phases of matter can be generated by performing random single-qubit measurements on a subsystem of toric code. Using a parton construction, such measurements map to random Gaussian tensor networks, and in particular,…
We define a measuring device (detector) of the coordinate of quantum particle as an absorbing wall that cuts off the particle's wave function. The wave function in the presence of such detector vanishes on the detector. The trace the…
Superposition is an essential feature of quantum mechanics. From the Schrodinger's cat to quantum algorithms such as Deutsch-Jorsza algorithm, quantum superposition plays an important role. It is one fundamental and crucial question how to…
For a class of piecewise deterministic Markov processes we introduce a stochastic calculus which is a certain non-Gaussian counterpart to the classical Malliavin calculus. As an application we investigate the regularity of densities of…
In a series of papers Tsirelson constructed from measure types of random sets and generalised random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…