We show that the evolution of the wave functions in the PT symmetric quantum mechanics is pseudo-unitary. Their pseudo-norm 〈ψ|P|ψ〉 remains time-independent. This persists even if the PT symmetry itself becomes spontaneously broken. PACS 03.65.Bz, 03.65.Ca 03.65.Fd February 3, 2008, spon.tex file

It is shown that the baryon magnetic moment descriptions in the frameworks of the chiral model ChPT and the quark soliton χQSM one are practically identical. The main difference from the traditional unitary symmetry models proves to be in terms due to the pionic current contribution into the magnetic moments of nucleons and in the prediction for the Λ magnetic moment.

We draw some rigorous conclusions about the functional properties of the μ − ρ relation in the Hubbard model based on symmetry considerations and unitary transformations. It is shown that the charge susceptibility reaches its local extreme at half-filling. Exact expressions are obtained in two limiting cases. PACS number(s): 75.10.Lp,71.20.Ad,74.65.+n,74.20.Mn

Using the Fokker-Planck equation describing trie evolution of the transmission eigenvalues for Dyson's Brownian motion ensemble, we calculate the magnetoconductance of a ballistic chaotic dot in m the crossover regime from the orthogonal to the unitary symmetry. The correlation functions of the transmission eigenvalues are expressed in terms of quaternion determinants for arbitrary number N of ...

Abstract: The invariance under unitary representations of the conformal group SL(2,R) of a quantum particle is rigorously investigated in two-dimensional spacetimes containing Killing horizons using de Alfaro-Fubini-Furlan’s model. The limit of the near-horizon approximation is considered. If the Killing horizon is bifurcate (Schwarzschild-like near horizon limit), the conformal symmetry is hid...

Following the newly formulated notion of form invariance of the neutrino mass matrix, a complete model of leptons is constructed. It is based on a specific unitary 3 × 3 matrix U in family space, such that U is the simple discrete symmetry νe → −νe, νμ ↔ ντ . Thus U also generates the cyclic group Z4. The charged-lepton mass matrix is nearly diagonal while the neutrino mass matrix is of the for...

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of...

The path integral of a gauge theory is studied in Coulomb-like gauges. The Christ-Lee terms of operator ordering are reproduced within the path integration framework. In the presence of fermions, a new operator term, in addition to that of Christ-Lee, is discovered. Such kind of terms is found to be instrumental in restoring the invariance of the effective Lagrangian under a field dependent gau...

On the one hand, we put in evidence new symmetry operators of the nonlinear Korteweg-de Vries equation by exploiting its Lax form expressed in terms of a pair of linear equations. A KdV supersymmetric version is also studied in order to determine its symmetry Lie superalgebra. On the other hand, nonlinear sl(2)-algebras are then visited and new unitary irreducible representations are characteri...

We study state-sum constructions of G-equivariant spin-TQFTs and their relationship to Matrix Product States. We show that in the Neveu-Schwarz, Ramond, and twisted sectors, the states of the theory are generalized Matrix Product States. We apply our results to revisit the classification of fermionic Short-Range-Entangled phases with a unitary symmetry G and determine the group law on the set o...