Complete Dynamical Localization in Disordered Quantum Multi-Particle Systems (2009)
Aizenman, Michael, Warzel, Simone
We present some recent results concerning the persistence of dynamical localization for disordered systems of n particles under weak interactions.
Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder (2009)
Greenblatt, Rafael L., Aizenman, Michael, Lebowitz, Joel L.
We prove that the addition of an arbitrarily small random perturbation of a suitable type to a quantum spin system rounds a first order phase transition in the conjugate order parameter in d
Michael Aizenman, Sheldon Goldstein
Abstract. We prove that any stationary state describing an infinite classical system which is "stable " under local perturbations (and possesses some strong time clustering...
16th International Congress on Mathematical Physics (2008)
Aizenman, Michael, Daubechies, Ingrid, Exner, Pavel, Froehlich, Juerg, Gallavotti, Giovanni, Sinai, Yakov, ...
Localization Bounds for Multiparticle Systems (2008)
Aizenman, Michael, Warzel, Simone
We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes...
On the Joint Distribution of Energy Levels of Random Schroedinger Operators (2008)
Aizenman, Michael, Warzel, Simone
We consider operators with random potentials on graphs, such as the lattice version of the random Schroedinger operator. The main result is a general bound on the probabilities of simultaneous...
Michael Aizenman, Jeffrey H. Schenker, Roland M. Friedrich, Dirk Hundertmark
A technically convenient signature of localization, exhibited by discrete operators with random potentials, is exponential decay of the fractional moments of the Green function within the appropriate...
On the Structure of Quasi-Stationary Competing Particles Systems (2007)
Arguin, Louis-Pierre, Aizenman, Michael
We study point processes on the real line whose configurations X are locally finite, have a maximum, and evolve through increments which are functions of correlated gaussian variables. The...
Aizenman, Michael, Germinet, Francois, Klein, Abel, Warzel, Simone
As was noted already by A. N. Kolmogorov, any random variable has a Bernoulli component. This observation provides a tool for the extension of results which are known for Bernoulli random variables...
Mean-Field Spin Glass models from the Cavity--ROSt Perspective (2006)
Aizenman, Michael, Sims, Robert, Starr, Shannon L.
The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The...
Perspectives in Statistical Mechanics (2006)
Without attempting to summarize the vast field of statistical mechanics, we briefly mention some of the progress that was made in areas which have enjoyed Barry Simon's interests. In particular, we...
The Canopy Graph and Level Statistics for Random Operators on Trees (2006)
Aizenman, Michael, Warzel, Simone
For operators with homogeneous disorder, it is generally expected that there is a relation between the spectral characteristics of a random operator in the infinite setup and the distribution of the...
On the Critical Behavior at the Lower Phase Transition of the Contact Process (2006)
We present general results for the contact process by a method which applies to all transitive graphs of bounded degree, including graphs of exponential growth. The model's infection rates are varied...
From Finite-System Entropy to Entropy Rate for a (2006)
Or Zuk, Student Member, Eytan Domany, Ido Kanter, Michael Aizenman
Abstract—A recent result presented the expansion for the entropy rate of a hidden Markov process (HMP) as a power series in the noise variable. The coefficients of the expansion around the...
From Finite-System Entropy to Entropy Rate for a (2006)
Or Zuk, Eytan Domany, Ido Kanter, Michael Aizenman
A recent result presented the expansion for the entropy rate of a Hidden Markov Process (HMP) as a power series in the noise variable ɛ. The coefficients of the expansion around the noiseless (ɛ =...
Fluctuation based proof of the stability of ac spectra of random operators on tree graphs (2005)
Aizenman, Michael, Sims, Robert, Warzel, Simone
We summarize recent works on the stability under disorder of the absolutely continuous spectra of random operators on tree graphs. The cases covered include: Schr\"odinger operators with random...
From finite-system entropy to entropy rate for a Hidden Markov Process (2005)
Zuk, Or, Domany, Eytan, Kanter, Ido, Aizenman, Michael
A recent result presented the expansion for the entropy rate of a Hidden Markov Process (HMP) as a power series in the noise variable $\eps$. The coefficients of the expansion around the noiseless...
Taylor series expansions for the entropy rate of Hidden Markov Processes (2005)
Zuk, Or, Domany, Eytan, Kanter, Ido, Aizenman, Michael
Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the...
Aizenman, Michael, Warzel, Simone
We consider radial tree extensions of one-dimensional quasi-periodic Schroedinger operators and establish the stability of their absolutely continuous spectra under weak but extensive perturbations...
Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder (2005)
Aizenman, Michael, Sims, Robert, Warzel, Simone
We consider the Laplacian on a rooted metric tree graph with branching number $ K \geq 2 $ and random edge lengths given by independent and identically distributed bounded variables. Our main result...
Aizenman, Michael, Sims, Robert, Warzel, Simone
The subject of this work are random Schroedinger operators on regular rooted tree graphs $\T$ with stochastically homogeneous disorder. The operators are of the form $H_\lambda(\omega) = T + U +...
Characterization of invariant measures at the leading edge for competing particle systems (2005)
Ruzmaikina, Anastasia, Aizenman, Michael
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. “Quasi-stationary states” are defined as probability measures, on the...
Characterization of invariant measures at the leading edge for competing particle systems (2004)
Ruzmaikina, Anastasia, Aizenman, Michael
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the...
Bose-Einstein Quantum Phase Transition in an Optical Lattice Model (2004)
Aizenman, Michael, Lieb, Elliott H., Seiringer, Robert, Solovej, Jan Philip, Yngvason, Jakob
Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an external potential, such as that presented by an optical lattice. We present a model of this phenomenon which we are able...
B.: Adiabatic charge transport and the Kubo formula for Landau Type Hamiltonians (2004)
Michael Aizenman, Alexander Elgart, H. Schenker
Abstract. We study adiabatic charge transport in a two dimensional lattice model of electron gas at zero temperature. It is proved that if the Fermi level falls in the localization regime then, for a...
Fractional Moment Methods for Anderson Localization in the Continuum (2003)
Aizenman, Michael, Elgart, Alexander, Naboko, Sergey, Schenker, Jeffrey H., Stolz, Günter
The fractional moment method, which was initially developed in the discrete context for the analysis of the localization properties of lattice random operators, is extended to apply to random...
Moment Analysis for Localization in Random Schroedinger Operators (2003)
Aizenman, Michael, Elgart, Alexander, Naboko, Serguei, Schenker, Jeffrey H., Stolz, Gunter
We study localization effects of disorder on the spectral and dynamical properties of Schroedinger operators with random potentials. The new results include exponentially decaying bounds on the...
An Extended Variational Principle for the SK Spin-Glass Model (2003)
Aizenman, Michael, Sims, Robert, Starr, Shannon L.
The recent proof by F. Guerra that the Parisi ansatz provides a lower bound on the free energy of the SK spin-glass model could have been taken as offering some support to the validity of the...
WITHDRAWN: Adiabatic charge transport and the Kubo formula for 2D Hall conductance (2002)
Aizenman, Michael, Elgart, Alexander, Schenker, Jeffrey H.
This paper has been withdrawn by the authors, due to an error in the proof of Lemma 3.1.
The Creation of Spectral Gaps by Graph Decoration (2000)
Schenker, Jeffrey H., Aizenman, Michael
We present a mechanism for the creation of gaps in the spectra of self-adjoint operators defined over a Hilbert space of functions on a graph, which is based on the process of graph decoration. The...
The creation of spectral gaps by graph decoration (2000)
Jeffrey H. Schenker, Michael Aizenman
Abstract. We present a mechanism for the creation of gaps in the spectra of self-adjoint operators defined over a Hilbert space of functions on a graph, which is based on the process of graph...
Finite-Volume Fractional-Moment Criteria for Anderson Localization (1999)
Aizenman, Michael, Schenker, Jeffrey H., Friedrich, Roland M., Hundertmark, Dirk
A technically convenient signature of localization, exhibited by discrete operators with random potentials, is exponential decay of the fractional moments of the Green function within the appropriate...
Path Crossing Exponents and the External Perimeter in 2D Percolation (1999)
Aizenman, Michael, Duplantier, Bertrand, Aharony, Amnon
2D Percolation path exponents $x^{\cal P}_{\ell}$ describe probabilities for traversals of annuli by $\ell$ non-overlapping paths, each on either occupied or vacant clusters, with at least one of...
Scaling Limits for Minimal and Random Spanning Trees in Two Dimensions (1998)
Aizenman, Michael, Burchard, Almut, Newman, Charles M., Wilson, David B.
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a...
Continuum Limits for Critical Percolation and Other Stochastic Geometric Models (1998)
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the...
H\"older Regularity and Dimension Bounds for Random Curves (1998)
Aizenman, Michael, Burchard, Almut
Random systems of curves exhibiting fluctuating features on arbitrarily small scales ($\delta$) are often encountered in critical models. For such systems it is shown that scale-invariant bounds on...
On the number of incipient spanning clusters (1997)
Abstract In critical percolation models, in a large cube there will typically be more than one cluster of comparable diameter. In 2D, the probability of −α k2 k>> 1 spanning clusters is of...
Scaling Limit for the Incipient Spanning Clusters (1996)
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A...
On the Number of Incipient Spanning Clusters (1996)
In critical percolation models, in a large cube there will typically be more than one cluster of comparable diameter. In 2D, the probability of $k>>1$ spanning clusters is of the order $e^{-\alpha...
On the Number of Incipient Spanning Clusters (1996)
In critical percolation models, in a large cube there will typically be more than one cluster of comparable diameter. In 2D, the probability of k ?? 1 spanning clusters is of the order e \Gammaff k 2...
For spin models with O(2)-invariant ferromagnetic interactions, the PatrascioiuSeiler constraint is: |arg(S(x))-arg(S(y))| ² q o for all |x-y|=1. It is shown that in two dimensional systems of...
Geometric Aspects of Quantum Spin States (1993)
Aizenman, Michael, Nachtergaele, Bruno
A number of interesting features of the ground states of quantum spin chains are analized with the help of a functional integral representation of the system's equilibrium states. Methods of general...
Mathematical Physics Geometric Aspects of Quantum Spin States (1993)
Michael Aizenman, Bruno Nachtergaele
Abstract: A number of interesting features of the ground states of quantum spin chains are analyzed with the help of a functional integral representation of the system's equilibrium states....
Localization at Weak Disorder: Some Elementary Bounds (1993)
An elementary proof is given of localization for linear operators H=H o +lV, with H o translation invariant, or periodic, and V( . ) a random potential, in energy regimes which for weak disorder...
On the equivalence between KMS-states and equilibrium states for classical systems (1977)
Aizenman, Michael, Goldstein, Sheldon, Gruber, Christian, Lebowitz, Joel L., Martin, Philippe A.
Stability and equilibrium states of infinite classical systems (1976)
Aizenman, Michael, Gallavotti, Giovanni, Goldstein, Sheldon, Lebowitz, Joel L.
Geometric Aspects of Quantum Spin States
Michael Aizenman, Bruno Nachtergaele, Where P
A number of interesting features of the ground states of quantum spin chains are analized with the help of a functional integral representation of the system 's equilibrium states. Methods of...