NSF-ITP-96-127 hep-th/9610009 Fermion Bags in the Massive Gross-Neveu Model (2009)
As has long been known, it is energetically favorable for massive fermions to deform the homogeneous vacuum around them, giving rise to extended bag-like objects. We study this phenomenon...
Statistics of Resonances in One Dimensional Continuous Systems (2009)
We study the average density of resonances (DOR) of a disordered one-dimensional continuous open system. The disordered system is semi-infinite, with white-noise random potential, and it is coupled...
Probabilistic Interpretation of Resonant States (2009)
Hatano, Naomichi, Kawamoto, Tatsuro, Feinberg, Joshua
We provide probabilistic interpretation of resonant states. This we do by showing that the integral of the modulus square of resonance wave functions (i.e., the conventional norm) over a properly...
Chaotic systems in complex phase space (2008)
Bender, Carl M., Feinberg, Joshua, Hook, Daniel W., Weir, David J.
This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in...
Junginger, Friederike, Kläui, Mathias, Backes, Dirk, Krzyk, Stephen, Rüdiger, Ulrich, Kasama, Takeshi, ...
In this paper, we present a complete three-dimensional characterization of vortex core spin structures, which is important for future magnetic data storage based on vortex cores in disks and in...
Does the complex deformation of the Riemann equation exhibit shocks? (2007)
Bender, Carl M., Feinberg, Joshua
The Riemann equation $u_t+uu_x=0$, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This equation is $\cP\cT$...
I review aspects of work done in collaboration with A. Zee and R. Scalettar \cite{fz1,fz2,fsz} on complex non-hermitean random matrices. I open by explaining why the bag of tools used regularly in...
Scaling and Universality of the Complexity of Analog Computation (2005)
Avizrats, Yaniv, Feinberg, Joshua, Fishman, Shmuel
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming...
Feinberg, Joshua, Hillel, Shlomi
Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We report here on our non-perturbative analysis of this phenomenon in the 1+1 dimensional massive...
Stable Fermion Bag Solitons in the Massive Gross-Neveu Model: Inverse Scattering Analysis (2005)
Feinberg, Joshua, Hillel, Shlomi
Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We study this phenomenon non-perturbatively in the 1+1 dimensional Massive Gross-Neveu model, in the...
A Universal Scaling Theory for Complexity of Analog Computation (2005)
Avizrats, Yaniv S., Feinberg, Joshua, Fishman, Shmuel
We discuss the computational complexity of solving linear programming problems by means of an analog computer. The latter is modeled by a dynamical system which converges to the optimal vertex...
Quantized Normal Matrices: Some Exact Results and Collective Field Formulation (2004)
We formulate and study a class of U(N)-invariant quantum mechanical models of large normal matrices with arbitrary rotation-invariant matrix potentials. We concentrate on the U(N) singlet sector of...
We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the $n$th and $n-1$th minors, whose solution is a...
The Response to a Perturbation in the Reflection Amplitude (2004)
We apply inverse scattering theory to calculate the functional derivative of the potential $V(x)$ and wave function $\psi(x,k)$ of a one-dimensional Schr\"odinger operator with respect to the...
All about the Static Fermion Bags in the Gross-Neveu Model (2003)
We review in detail the construction of {\em all} stable static fermion bags in the 1+1 dimensional Gross-Neveu model with $N$ flavors of Dirac fermions, in the large $N$ limit. In addition to the...
Marginally Stable Topologically Non-Trivial Solitons in the Gross-Neveu Model (2002)
We show that a kink and a topologically trivial soliton in the Gross-Neveu model form, in the large-N limit, a marginally stable static configuration, which is bound at threshold. The energy of the...
Consider random matrices $A$, of dimension $m\times (m+n)$, drawn from an ensemble with probability density $f(\rmtr AA^\dagger)$, with $f(x)$ a given appropriate function. Break $A = (B,X)$ into an...
The periodic table of static fermion bags in the Gross-Neveu Model (2002)
We study the spectrum of stable static fermion bags in the 1+1 dimensional Gross-Neveu model with $N$ flavors of Dirac fermions, in the large $N$ limit. In the process, we discover a new kink,...
Probabilistic analysis of the phase space flow for linear programming (2001)
Ben-Hur, Asa, Feinberg, Joshua, Fishman, Shmuel, Siegelmann, Hava T.
The phase space flow of a dynamical system leading to the solution of Linear Programming (LP) problems is explored as an example of complexity analysis in an analog computation framework. An ensemble...
Probabilistic analysis of a differential equation for linear programming (2001)
Ben-Hur, Asa, Feinberg, Joshua, Fishman, Shmuel, Siegelmann, Hava T.
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a...
We show that the spectral theory of the Dirac operator $D = i\delsl-\sigma(x) -i\pi(x)\gam_5$ in a static background $(\sigma(x),\pi(x))$ in 1+1 space-time dimensions, is underlined by a certain...
We study static fermion bags in the 1+1 dimensional Gross-Neveu and Nambu-Jona-Lasinio models. It has been known, from the work of Dashen, Hasslacher and Neveu (DHN), followed by Shei's work, in the...
"Single Ring Theorem" and the Disk-Annulus Phase Transition (2001)
Feinberg, Joshua, Scalettar, R., Zee, A.
Recently, an analytic method was developed to study in the large $N$ limit non-hermitean random matrices that are drawn from a large class of circularly symmetric non-Gaussian probability...
Finite Temperature Effective Action in Monopole Background (1999)
Dunne, Gerald, Feinberg, Joshua
We compute the CP-odd part of the finite temperature effective action for massive Dirac fermions in the presence of a Dirac monopole. We confirm that the induced charge is temperature dependent, and...
Non-Hermitean Localization and De-Localization (1997)
We study localization and delocalization in a class of non-hermitean Hamiltonians inspired by the problem of vortex pinning in superconductors. In various simplified models we are able to obtain...
Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics (1997)
Dunne, Gerald, Feinberg, Joshua
We discuss supersymmetric quantum mechanical models with periodic potentials. The important new feature is that it is possible for both isospectral potentials to support zero modes, in contrast to...
Renormalizing Rectangles and Other Topics in Random Matrix Theory (1996)
We consider random Hermitian matrices made of complex or real $M\times N$ rectangular blocks, where the blocks are drawn from various ensembles. These matrices have $N$ pairs of opposite real...
We discuss minisuperspace aspects a non empty Robertson-Walker universe containing scalar matter field. The requirement that the Wheeler-DeWitt (WDW) operator be self adjoint is a key ingredient in...
Eigenvalue Integro-Differential Equations for Orthogonal Polynomials on the Real Line (1994)
Bender, Carl M., Feinberg, Joshua
The one-dimensional harmonic oscillator wave functions are solutions to a Sturm-Liouville problem posed on the whole real line. This problem generates the Hermite polynomials. However, no other set...
On Kinks and Bound States in the Gross-Neveu Model (1994)
We investigate static space dependent $\sigx=\lag\bar\psi\psi\rag$ saddle point configurations in the two dimensional Gross-Neveu model in the large N limit. We solve the saddle point condition for...
We discuss O(N) invariant scalar field theories in 0+1 and 1+1 space-time dimensions. Combining ordinary ``Large N" saddle point techniques and simple properties of the diagonal resolvent of one...
The one dimensional Fermi gas of matrix eigenvalues of the Marinari-Parisi model at positive values of the cosmological constant is generalised.The number of matrix eigenvalues (i.e. gas particles)...
Stabilised Matrix Models for Non-Perturbative Two Dimensional Quantum Gravity (1992)
A thorough analysis of stochastically stabilised hermitian one matrix models for two dimensional quantum gravity at all its $(2,2k-1)$ multicritical points is made. It is stressed that only the zero...
String Field Theory for d \leq 0 Matrix Models via Marinari-Parisi (1992)
We generalize the Marinari-Parisi definition for pure two dimensional quantum gravity $(k = 2)$ to all non unitary minimal multicritical points $(k \geq 3)$. The resulting interacting Fermi gas...