相关论文: Time Ordering, Energy Ordering, and Factorization

The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable…

We consider algorithms for the factorization of linear partial differential operators. We introduce several new theoretical notions in order to simplify such considerations. We define an obstacle and a ring of obstacles to factorizations.…

In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many…

Recently, a thermodynamic definition of time has been introduced. This definition is useful to find approach some open problems in physics. But, it was obtained by a phenomenological approach and a logical inconsistency appears in the…

It is shown that calculation of the operator's groups product with the independent time ordering procedure in each one is important for some problems in the nonequilibrium quantum field theory at finite temperature. This problem is solved…

We treat collaborative filtering as a univariate time series estimation problem: given a user's previous votes, predict the next vote. We describe two families of methods for transforming data to encode time order in ways amenable to…

The inverse relationship between energy and time is as familiar as Planck's constant. From the point of view of a system with many states, perhaps a better representation of the system is a vector of characteristic times (one per state) for…

The relationship between 'information' and 'time' is explored in order to look for a 'solution' to the 'Problem of Time'. 'Time' is found to be the result of the conversion of energy into 'information'. The 'time' number or label we assign…

Resources and their use and consumption form a central part of our life. Many branches of science and engineering are concerned with the question of which given resource objects can be converted into which target resource objects. For…

Active matter encompasses systems whose individual consituents dissipate energy to exert propelling forces on their environment. This rapidly developing field harbors a dynamical phenomenology with no counterpart in passive systems. The…

Multivariate time series classification is a task with increasing importance due to the proliferation of new problems in various fields (economy, health, energy, transport, crops, etc.) where a large number of information sources are…

Prime factorization is an outstanding problem in arithmetic, with important consequences in a variety of fields, most notably cryptography. Here we employ the intriguing analogy between prime factorization and optical interferometry in…

We consider the energy representation for the gauge group. The gauge group is the set of (C^{\infty})-mappings from a compact Riemannian manifold to a semi-simple compact Lie group. In this paper, we obtain irreducibility of the energy…

Positive-definite matrices materialize as state transition matrices of linear time-invariant gradient flows, and the composition of such materializes as the state transition after successive steps where the driving potential is suitably…

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed,…

We develop first steps in the study of factorizations of elements in ultraproducts of commutative cancellative monoids into irreducible elements. A complete characterization of the (multi-)sets of lengths in such objects is given. As…

We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.

The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation…

In mathematical modeling of the non-squared frequency-dependent diffusions, also known as the anomalous diffusions, it is desirable to have a positive real Fourier transform for the time derivative of arbitrary fractional or odd integer…

A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…