We consider photons strongly coupled to the excitonic excitations of a quantum well, in presence an electric field. show how, under field increase, hybrid polariton made photon carriers lying two wells transforms into dipolariton direct and indirect excitons. also how cavity lifetime coherence time carrier wave vectors that we analytically handle through non-hermitian Hamiltonians affect these ...

For a separable rearrangement invariant space X on $$(0,\infty )$$ of fundamental type we identify the set all $$p\in [1,\infty ]$$ such that $$\ell ^p$$ is finitely represented in way unit basis vectors ( $$c_0$$ if $$p=\infty $$ ) correspond to pairwise disjoint and equimeasurable functions. This characterization hinges upon description approximate eigenvalues doubling operator $$x(t)\mapsto ...

The eigenvalues of a nonhermitian Toeplitz matrix A are usually highly sensitive to perturbations, having condition numbers that increase exponentially with the dimension N. An equivalent statement is that the resolvent ( ZZ A)’ of a Toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest-exponentially large as a function of N, even when z is far from the spectrum. B...

Given p-dimensional Gaussian vectors Xi iid ∼ N(0,Σ), 1 ≤ i ≤ n, where p ≥ n, we are interested in testing a null hypothesis where Σ = Ip against an alternative hypothesis where all eigenvalues of Σ are 1, except for r of them are larger than 1 (i.e., spiked eigenvalues). We consider a Rare/Weak setting where the spikes are sparse (i.e., 1 r p) and individually weak (i.e., each spiked eigenvalu...

The Common Vector (CV) method is a successful method which has been originally proposed for isolated word recognition problems in the case where the number of samples for each class is less than or equal to the dimensionality of the sample space. This method suggests elimination of all the features that are in the direction of the eigenvectors corresponding to the nonzero eigenvalues of the cov...

Abstract—The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state...

We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(n)), Y(gl(m|n)), Ûq(gl(n)) or Ûq(gl(m|n)) (super)algebras, with arbitrary representations (i.e. ‘spins’) on each site of the chain and diagonal boundary matrices (K+(u),K−(u)). The nested Bethe anstaz applies for a general K−(u), but a particular form of the K+(u) matrix. The construction extend...

We take the Bose–Hubbard model to illustrate exact diagonalization techniques in a pedagogical way. We follow the route of first generating all the basis vectors, then setting up the Hamiltonian matrix with respect to this basis and finally using the Lanczos algorithm to solve low lying eigenstates and eigenvalues. Emphasis is placed on how to enumerate all the basis vectors and how to use the ...

Identification of the channel matrix is of main concern in wireless MIMO (Multiple Input Multiple Output) systems. To maximize the SNR, the best way to utilize a MIMO system is to communicate on the top singular vectors of the channel matrix. Here, we present a new approach for direct blind identification of the main independent singular modes, without first estimating the channel matrix itself...

is called the discrepancy of (xn)n=1. In 1954 Roth (see [DrTi], [KN]) proved that for any sequence in [0, 1) limN→∞ND(N)/ log N > 0. (2) Let A be an s × s invertible matrix with integer entries. A matrix A is said to be ergodic if for almost all α ∈ R the sequence {αA}n≥1 is uniformly distributed. A vector α ∈ R is said to be normal (A normal) if the sequence {αA}n≥1 is uniformly distributed. L...