Péter Lévay - Academia.edu (original) (raw)

Papers by Péter Lévay

arXiv (Cornell University), Dec 2, 2003

Acta Physica Hungarica A) Heavy Ion Physics, 1997

Lecture Notes in Physics, 1994

The modified Newton-Sabatier method is applied to invert electron-atom scattering phase-shifts in... more The modified Newton-Sabatier method is applied to invert electron-atom scattering phase-shifts into effective potentials. The long range (–/2r4) tail of the polarization interaction requires a special treatment. Examples involving inversion of synthetic as well as experimental phase-shifts are presented.

Encyclopedia of Mathematical Physics, 2006

Journal of Physics B: Atomic, Molecular and Optical Physics, 1988

The Kohn and Schwinger variational methods are applied to electron scattering by local spherical ... more The Kohn and Schwinger variational methods are applied to electron scattering by local spherical potentials and the numerical results are compared with those of Ladanyi's method (1970) based on the standard form of the Schrodinger equation. Both the stability and the convergence of the results are carefully analysed and, in the case of Ladanyi's method, the measure of the error of the approximate solution is investigated as well. The analysis implies that Ladanyi's method is competitive in comparison with the standard variational procedures.

Journal of Physics A: Mathematical and General, 1994

Coupled systems of slow and fast variables with symmetry, characterized by a semisimple Lie group... more Coupled systems of slow and fast variables with symmetry, characterized by a semisimple Lie group G, are employed to study the effect of adiabatic decoupling of the fast degrees of freedom on the algebra of symmetry generators. The slow configuration space is assumed to be the symmetric coset space G/H, where H is a compact subgroup of G defined by the fast Hamiltonian. The induced gauge fields characterizing the effective slow dynamics are symmetric ones in the sense that the action of G on them can be compensated by an H-valued gauge transformation. The modification of the symmetry generators when such gauge fields are present can be described purely in geometric terms related to the non-Abelian geometric phase. The modified generators may be identified as the generators of the induced representation of G, where the inducing represention is the representation of H on the fast Hilbert space. This result enables us to recast the problem of exotic quantum numbers for effective quantum systems in purely algebraic terms via the Frobenius reciprocity theorem. Illustrative calculations for the symmetric spaces SO(d+1)/SO(d) approximately Sd (spheres) are presented. Possible relevance of modified generators for non-compact G for obtaining scattering potentials in the framework of algebraic scattering theory is also pointed out.

Journal of Physics A: Mathematical and General, 1995

Using a first-order Casimir operator calculated in a non-standard realization for the so(3,1) alg... more Using a first-order Casimir operator calculated in a non-standard realization for the so(3,1) algebra, we obtain a one-dimensional scattering problem with LS-type interaction terms. It is shown that for this realization the square of this operator can be expressed in terms of the usual quadratic Casimir. Due to this constraint the scattering states are completely specified by restricting the possible set of eigenvalues accordingly. The results show that the use of extra Casimir operators can provide additional insight into the group theoretical structure of the scattering problem. A generalization for the so(2n-1,1), n>2 case is also given. The underlying supersymmetry of the resulting Schrodinger equations is pointed out. The supersymmetric charge operators are related to our first-order Casimir operators.

International Journal of Geometric Methods in Modern Physics, 2010

It is shown that the Veldkamp space of the unique generalized quadrangle GQ(2, 4) is isomorphic t... more It is shown that the Veldkamp space of the unique generalized quadrangle GQ(2, 4) is isomorphic to PG(5, 2). Since the GQ(2, 4) features only two kinds of geometric hyperplanes, namely point's perp-sets and GQ(2, 2)s, the 63 points of PG(5, 2) split into two families; 27 being represented by perp-sets and 36 by GQ(2, 2)s. The 651 lines of PG(5, 2) are found to fall into four distinct classes: in particular, 45 of them feature only perp-sets, 216 comprise two perp-sets and one GQ(2, 2), 270 consist of one perp-set and two GQ(2, 2)s and the remaining 120 are composed solely of GQ(2, 2)s, according to the intersection of two distinct hyperplanes determining the (Veldkamp) line is, respectively, a line, an ovoid, a perp-set and a grid (i.e. GQ(2, 1)) of a copy of GQ(2, 2). A direct "by-hand" derivation of the above-listed properties is followed by their heuristic justification based on the properties of an elliptic quadric of PG(5, 2) and complemented by a proof employing ...

EPL (Europhysics Letters), 2012

Employing the fact that the geometry of the N-qubit (N≥2) Pauli group is embodied in the structur... more Employing the fact that the geometry of the N-qubit (N≥2) Pauli group is embodied in the structure of the symplectic polar space W(2N−1,2) and using properties of the Lagrangian Grassmannian LGr(N,2N) defined over the smallest Galois field, it is demonstrated that there exists a bijection between the set of maximum sets of mutually commuting elements of the N-qubit Pauli group and a certain subset of elements of the 2N−1-qubit Pauli group. In order to reveal finer traits of this correspondence, the cases N=3 (also addressed recently by Lévay, Planat and Saniga (JHEP 09 (2013) 037)) and N=4 are discussed in detail. As an apt application of our findings, we use the stratification of the ambient projective space PG(2N−1,2) of the 2N−1-qubit Pauli group in terms of G-orbits, where G≡SL(2,2)×SL(2,2)×⋅⋅⋅×SL(2,2)⋊SN, to decompose π––(LGr(N,2N)) into non-equivalent orbits. This leads to a partition of LGr(N,2N) into distinguished classes that can be labeled by elements of the above-mentione...

Abstract: It is shown that the E 6(6) symmetric entropy formula describing black holes and black ... more Abstract: It is shown that the E 6(6) symmetric entropy formula describing black holes and black strings in D = 5 is intimately tied to the geometry of the generalized quadrangle GQ(2, 4) with automorphism group the Weyl group W(E6). The 27 charges correspond to the points and the 45 terms in the entropy formula to the lines of GQ(2, 4). Different truncations with 15, 11 and 9 charges are represented by three distinguished subconfigurations of GQ(2, 4), well-known to finite geometers; these are the “doily ” (i. e. GQ(2, 2)) with 15, the “perp-set ” of a point with 11, and the “grid ” (i. e. GQ(2, 1)) with 9 points, respectively. In order to obtain the correct signs for the terms in the entropy formula, we use a non-commutative labelling for the points of GQ(2, 4). For the 40 different possible truncations with 9 charges this labelling yields 120 Mermin squares — objects well-known from studies concerning Bell-Kochen-Specker-like theorems. These results are connected to our previous ...