arXiv subjects

S. L. Adler

Publications and source records attributed to S. L. Adler.

8 recordsLinked to original sources

arXiv2004

Towards Quantum Superpositions of a Mirror: an Exact Open Systems Analysis - Calculational Details

We give details of calculations analyzing the proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester within different stochastic models for state vector collapse. We give two methods for exactly calculating the fringe visibility in these models, one proceeding directly from the equation of motion for the expectation of the density matrix, and the other proceeding from solving a linear stochastic unravelling of this equation. We also give details of the calculation that identifies the stochasticity parameter implied by the small displacement Taylor expansion of the CSL model density matrix equation. The implications of the two results are briefly discussed. Two pedagogical appendices review mathematical apparatus needed for the calculations.

quant-ph↗

arXiv2001

Martingale Models for Quantum State Reduction

Stochastic models for quantum state reduction give rise to statistical laws that are in most respects in agreement with those of quantum measurement theory. Here we examine the correspondence of the two theories in detail, making a systematic use of the methods of martingale theory. An analysis is carried out to determine the magnitude of the fluctuations experienced by the expectation of the observable during the course of the reduction process and an upper bound is established for the ensemble average of the greatest fluctuations incurred. We consider the general projection postulate of Lüders applicable in the case of a possibly degenerate eigenvalue spectrum, and derive this result rigorously from the underlying stochastic dynamics for state reduction in the case of both a pure and a mixed initial state. We also analyse the associated Lindblad equation for the evolution of the density matrix, and obtain an exact time-dependent solution for the state reduction that explicitly exhibits the transition from a general initial density matrix to the Lüders density matrix. Finally, we apply Girsanov's theorem to derive a set of simple formulae for the dynamics of the state in terms of a family of geometric Brownian motions, thereby constructing an explicit unravelling of the Lindblad equation.

quant-ph↗

arXiv1997

A Model for the Quark Mass and Flavor Mixing Matrices Based on Discrete Chiral Symmetry as the Origin of Families

We construct a model for the quark mass and flavor mixing matrices, based on the hypothesis that the flavor weak eigenstates in the three families are distinguished by a spontaneously broken discrete $Z_6$ chiral symmetry. In a leading partially symmetric approximation, the model accommodates the family mass spectra, with a CKM matrix that is exactly unity. Adding small asymmetries in first order perturbation theory gives a CKM matrix with the correct qualitative structure, with $s_{23}/s_{12}$ and $s_{13}/s_{12}$ naturally of order $M_s/M_b$.

hep-ph↗

arXiv1996

Response to the Comment by G. Emch on Projective Group Representations in Quaternionic Hilbert Space

We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embeddings, and leads to a detailed theory of quaternionic, as well as complex, projective group representations.

hep-th↗

arXiv1994

Study of a New Neuron

We study a modular neuron alternative to the McCulloch-Pitts neuron that arises naturally in analog devices in which the neuron inputs are represented as coherent oscillatory wave signals. Although the modular neuron can compute $XOR$ at the one neuron level, it is still characterized by the same Vapnik-Chervonenkis dimension as the standard neuron. We give the formulas needed for constructing networks using the new neuron and training them using back-propagation. A numerical study of the modular neuron on two data sets is presented, which demonstrates that the new neuron performs at least as well as the standard neuron.

adap-org↗

arXiv1994

Algebraic and geometric aspects of generalized quantum dynamics

\noindent We briefly discuss some algebraic and geometric aspects of the generalized Poisson bracket and non--commutative phase space for generalized quantum dynamics, which are analogous to properties of the classical Poisson bracket and ordinary symplectic structure.

hep-th↗

arXiv1994

Composite leptons and quarks constructed as triply occupied quasiparticles in quaternionic quanutm mechanics

\noindent We propose a set of rules for constructing composite leptons and quarks as triply occupied quasiparticles, in the quaternionic quantum mechanics of a pair of Harari-Shupe preons $T$ and $V$. The composites fall into two classes, those with totally antisymmetric internal wave functions, and those with internal wave functions of mixed symmetry. The mixed symmetry states consist of precisely the three spin 1/2 quark lepton families used in the standard model (48 particle states, {\it not} counting the doubling arising from antiparticles), plus one doublet of spin 3/2 quarks (24 particle states). The antisymmetric states consist of a set of spin 3/2 leptonic states with charges as in a standard model family (16 particle states), and a spin 1/2 leptonic fractionally charged doublet (4 particle states). We sketch ideas for deriving our rules from a fundamental quaternionic preonic field theory.

hep-th↗

arXiv1993

Proof of Jacobi identity in generalized quantum dynamics

We prove that the Jacobi identity for the generalized Poisson bracket is satisfied in the generalization of Heisenberg picture quantum mechanics recently proposed by one of us (SLA). The identity holds for any combination of fermionic and bosonic fields, and requires no assumptions about their mutual commutativity.

hep-th↗