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We consider the statistics of overlaps between a mixed state and its image under random unitary transformations. Choosing the transformations from the unitary group with its invariant (Haar) measure, the distribution of overlaps depends…
Single-valuedness of the eigenfunctions of the quantised Hitchin Hamiltonians is proposed as a natural quantisation condition. Separation of Variables can be used to relate the classification of eigenstates to the classification of…
In this paper we establish that every (deterministic) non-autonomous, discrete-time, causal, time invariant system has a state-space representation, and discuss its minimality.
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…
Using the momentum constraint, the standard evolution system is written in a fully first order form. The class of first order invariant algebraic slicing conditions is considered. The full set of characteristic fields is explicitly given.…
Solutions of generic $SU(2)\otimes SU(2)$ Hamiltonian eigensystems are obtained through systematic manipulations of quartic polynomial equations. An {\em ansatz} for constructing separable and entangled eigenstate basis, depending on the…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
To what extent do individual eigenstates encode information of their underlying Hamiltonian, and how does this depend on their spectral position? For many-body quantum systems, this issue is widely understood in terms of the differing…
A method is presented for evaluating authors on the basis of citations. It assigns to each author a citation score which depends upon the number of times he is cited, and upon the scores of the citers. The scores are found to be the…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
The relationship between the Jordan structures of two matrices sufficiently close has been largely studied in the literature, among which a square matrix $A$ and its rank one updated matrix of the form $A+xb^*$ are of special interest. The…
We consider the concept of a local set of inference rules. A local rule set can be automatically transformed into a rule set for which bottom-up evaluation terminates in polynomial time. The local-rule-set transformation gives…
We analize the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well defined evolution, and a consistent quantum…
In this paper, we investigate the asymptotic behaviors of the extreme eigenvectors in a general spiked covariance matrix, where the dimension and sample size increase proportionally. We eliminate the restrictive assumption of the block…
In the recent paper \cite{1}, Denton et al. provided the eigenvector-eigenvalue identity for Hermitian matrices, and a survey was also given for such identity in the literature. The main aim of this paper is to present the identity related…
In many, if not every realistic sequential decision-making task, the decision-making agent is not able to model the full complexity of the world. The environment is often much larger and more complex than the agent, a setting also known as…
Cooling methods and particle slowers as well as accelerators are basic tools for fundamental research and applications in different fields and systems. We put forward a generic mechanism to scale the momentum of a particle, regardless of…
In this paper we solve the eigenvalue problem of stochastic Hamiltonian system with boundary conditions. Firstly, we extend the results in S. Peng \cite{peng} from time-invariant case to time-dependent case, proving the existence of a…
In this paper, we show that the eigenvectors of the zero Laplacian and signless Lapacian eigenvalues of a $k$-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an…
In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that…