1,826 research outputs found

### SU(2) Yang-Mills quantum mechanics of spatially constant fields

As a first step towards a strong coupling expansion of Yang-Mills theory, the
SU(2) Yang-Mills quantum mechanics of spatially constant gauge fields is
investigated in the symmetric gauge, with the six physical fields represented
in terms of a positive definite symmetric (3 x 3) matrix S. Representing the
eigenvalues of S in terms of elementary symmetric polynomials, the eigenstates
of the corresponding harmonic oscillator problem can be calculated analytically
and used as orthonormal basis of trial states for a variational calculation of
the Yang-Mills quantum mechanics. In this way high precision results are
obtained in a very effective way for the lowest eigenstates in the spin-0
sector as well as for higher spin. Furthermore I find, that practically all
excitation energy of the eigenstates, independently of whether it is a
vibrational or a rotational excitation, leads to an increase of the expectation
value of the largest eigenvalue , whereas the expectation values of the
other two eigenvalues, and , and also the component =
g of the magnetic field, remain at their vacuum values.Comment: 7 pages, 4 figure

### On the generation of random ensembles of qubits and qutrits Computing separability probabilities for fixed rank states

The question of the generation of random mixed states is discussed, aiming
for the computation of probabilistic characteristics of composite finite
dimensional quantum systems. Particularly, we consider the generation of the
random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and
compute the corresponding probabilities to find a separable state among the
states of a fixed rank

### On the stratifications of 2-qubits X-state space

The 7-dimensional family $\mathfrak{P}_X$ of so-called mixed X-states of
2-qubits is considered. Two types of stratification of 2-qubits $X-$state
space, i.e., partitions of $\mathfrak{P}_X\,$ into orbit types with respect to
the adjoint group actions, one of the global unitary group $G_X \subset SU(4)$
and another one under the action of the local unitary group $LG_X \subset G_X$,
is described. The equations and inequalities in the invariants of the
corresponding groups, determining each stratification component, are given

### On the family of Wigner functions for N-level quantum system

The family of unitary non-equivalent Weyl-Stratonovich kernels determining
the Wigner probability distribution function of an arbitrary N-level quantum
system is constructed

### Generalized Calogero-Moser-Sutherland models from geodesic motion on GL(n, R) group manifold

It is shown that geodesic motion on the GL(n, R) group manifold endowed with
the bi-invariant metric d s^2 = tr(g^{-1} d g)^2 corresponds to a
generalization of the hyperbolic n-particle Calogero-Moser-Sutherland model. In
particular, considering the motion on Principal orbit stratum of the SO(n, R)
group action, we arrive at dynamics of a generalized n-particle
Calogero-Moser-Sutherland system with two types of internal degrees of freedom
obeying SO(n, R) \bigoplus SO(n, R) algebra. For the Singular orbit strata of
SO(n, R) group action the geodesic motion corresponds to certain deformations
of the Calogero-Moser-Sutherland model in a sense of description of particles
with different masses. The mass ratios depend on the type of Singular orbit
stratum and are determined by its degeneracy. Using reduction due to discrete
and continuous symmetries of the system a relation to II A_n
Euler-Calogero-Moser-Sutherland model is demonstrated.Comment: 16 pages, LaTeX, no figures. V2: Typos corrected, two references
added. V3: Abstract changed, typos corrected, a few formulas and references
added. The presentation in the last section has been clarified and it was
restricted to the case of GL(3, R) group, the analysis of GL(4, R) will be
given elsewhere. V4: Minor corrections in the whole text, more formulas and
references added, accepted for publication in PL

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