Joel L. Lebowitz
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Joel L. Lebowitz has a total of 101 co-authors. Here are the top co-authors by number of shared publications:
- Sheldon Goldstein
The State University of New Jersey
18 shared publications - Eugene R. Speer
Department of Mathematics, Rutgers University, New Brunswick, USA
14 shared publications - Roderich Tumulka
Mathematics Institute, Eberhard Karls University Tübingen, Tübingen, Germany
14 shared publications - Stefano Olla
CEREMADE, Université Paris-Dauphine, PSL Research University, Paris, France
13 shared publications - Tomasz Komorowski
Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland
11 shared publications - Bernard Derrida
Collège de France
10 shared publications
Latest Publications
- Open Access
- 25 February 2026
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 193 (3) , 34
Convergent Power Series for Anharmonic Chain with Periodic Forcing
We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses, preventing equi-distribution of energy per degree of freedom. We extend this result to anharmonic perturbations with bounded second derivatives and boundary dissipation, proving that for small perturbations and non-resonant forcing, the dynamics converges to a periodic stationary state with energy exponentially localized uniformly in the system size. The perturbed periodic state is described by a convergent power type expansion in the strength of the anharmonicity. This excludes chaoticity induced by anharmonicity, independently of the size of the system. Our perturbative scheme can also be applied in higher dimensions.
- 25 February 2026
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 193 (3) , 34
Open AccessConvergent Power Series for Anharmonic Chain with Periodic Forcing
We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses, preventing equi-distribution of energy per degree of freedom. We extend this result to anharmonic perturbations with bounded second derivatives and boundary dissipation, proving that for small perturbations and non-resonant forcing, the dynamics converges to a periodic stationary state with energy exponentially localized uniformly in the system size. The perturbed periodic state is described by a convergent power type expansion in the strength of the anharmonicity. This excludes chaoticity induced by anharmonicity, independently of the size of the system. Our perturbative scheme can also be applied in higher dimensions.
- Open Access
Periodically Driven anharmonic chain: Convergent Power Series and Numerics
We investigate the long time behavior of a pinned chain of $2N+1$ oscillators, indexed by $x \in\{-N,\ldots, N\}$. The system is subjected to an external driving force on the particle at $x=0$, of period $θ=2π/ω$, and to frictional damping $γ>0$ at both endpoints $x=-N$ and $N$. The oscillators interact with a pinned and nearest neighbor harmonic plus anharmonic potentials of the form $\frac{ω_0^2 q_x^2}{2}+\frac12 (q_{x}-q_{x-1})^2 +ν\left[V(q_x)+U(q_x-q_{x-1}) \right]$, with $V''$ and $U''$ bounded and $ν\in \mathbb{R}$. We recall the recently proven convergence and the global stability of a perturbation series in powers of $ν$ for $|ν| < ν_0$, yielding the long time periodic state of the system. Here $ν_0$ depends only on the supremum norms of $V''$ and $U''$ and the distance of the set of non-negative integer multiplicities of $ω$ from the interval $[ω_0,\sqrt{ω_0^2+4}]$ - the spectrum of the infinite harmonic chain for $ν=0$. We describe also some numerical studies of this system going beyond our rigorous results.Open AccessPeriodically Driven anharmonic chain: Convergent Power Series and Numerics
We investigate the long time behavior of a pinned chain of $2N+1$ oscillators, indexed by $x \in\{-N,\ldots, N\}$. The system is subjected to an external driving force on the particle at $x=0$, of period $θ=2π/ω$, and to frictional damping $γ>0$ at both endpoints $x=-N$ and $N$. The oscillators interact with a pinned and nearest neighbor harmonic plus anharmonic potentials of the form $\frac{ω_0^2 q_x^2}{2}+\frac12 (q_{x}-q_{x-1})^2 +ν\left[V(q_x)+U(q_x-q_{x-1}) \right]$, with $V''$ and $U''$ bounded and $ν\in \mathbb{R}$. We recall the recently proven convergence and the global stability of a perturbation series in powers of $ν$ for $|ν| < ν_0$, yielding the long time periodic state of the system. Here $ν_0$ depends only on the supremum norms of $V''$ and $U''$ and the distance of the set of non-negative integer multiplicities of $ω$ from the interval $[ω_0,\sqrt{ω_0^2+4}]$ - the spectrum of the infinite harmonic chain for $ν=0$. We describe also some numerical studies of this system going beyond our rigorous results. - Open Access
PERIODICALLY DRIVEN ANHARMONIC CHAIN: CONVERGENT POWER SERIES AND NUMERICS
We investigate the long time behavior of a pinned chain of 2N + 1 oscillators, indexed by x ∈ {-N, . . . , N }. The system is subjected to an external driving force on the particle at x = 0, of period θ = 2π ω, and to frictional damping γ > 0 at both endpoints x = -N and N . The oscillators interact with a pinned and nearest neighbor harmonic plus anharmonic potentials of the form with V ′′ and U ′′ bounded and ν ∈ R. We recall the recently proven convergence and the global stability of a perturbation series in powers of ν for ν < ν 0 , yielding the long time periodic state of the system. Here ν 0 depends only on the supremum norms of V ′′ and U ′′ and the distance of the set of non-negative integer multiplicities of ω from the interval [ω 0 , ω 2 0 + 4] -the spectrum of the infinite harmonic chain for ν = 0. We describe also some numerical studies of this system going beyond our rigorous results.
Open AccessPERIODICALLY DRIVEN ANHARMONIC CHAIN: CONVERGENT POWER SERIES AND NUMERICS
We investigate the long time behavior of a pinned chain of 2N + 1 oscillators, indexed by x ∈ {-N, . . . , N }. The system is subjected to an external driving force on the particle at x = 0, of period θ = 2π ω, and to frictional damping γ > 0 at both endpoints x = -N and N . The oscillators interact with a pinned and nearest neighbor harmonic plus anharmonic potentials of the form with V ′′ and U ′′ bounded and ν ∈ R. We recall the recently proven convergence and the global stability of a perturbation series in powers of ν for ν < ν 0 , yielding the long time periodic state of the system. Here ν 0 depends only on the supremum norms of V ′′ and U ′′ and the distance of the set of non-negative integer multiplicities of ω from the interval [ω 0 , ω 2 0 + 4] -the spectrum of the infinite harmonic chain for ν = 0. We describe also some numerical studies of this system going beyond our rigorous results.
- 14 January 2025
- Published by American Physical Society (APS) in Physical Review A
- Vol. 111 (1)
Stationary states of boundary-driven quantum systems: Some exact results
- 14 January 2025
- Published by American Physical Society (APS) in Physical Review A
- Vol. 111 (1)
Stationary states of boundary-driven quantum systems: Some exact results
- 24 February 2024
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 191 (2) , 1-20
On the Behaviour of a Periodically Forced and Thermostatted Harmonic Chain
- 24 February 2024
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 191 (2) , 1-20
On the Behaviour of a Periodically Forced and Thermostatted Harmonic Chain
- 23 June 2023
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 402 (2) , 2031-2078
Non-perturbative Solution of the 1d Schrödinger Equation Describing Photoemission from a Sommerfeld Model Metal by an Oscillating Field
- 23 June 2023
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 402 (2) , 2031-2078
Non-perturbative Solution of the 1d Schrödinger Equation Describing Photoemission from a Sommerfeld Model Metal by an Oscillating Field
- Open Access
On the Conversion of Work into Heat: Microscopic Models and Macroscopic Equations
We summarize and extend some of the results obtained recently for the microscopic and macroscopic behavior of a pinned harmonic chain, with random velocity flips at Poissonian times, acted on by a periodic force {at one end} and in contact with a heat bath at the other end. Here we consider the case where the system is in contact with two heat baths at different temperatures and a periodic force is applied at any position. This leads in the hydrodynamic limit to a heat equation for the temperature profile with a discontinuous slope at the position where the force acts. Higher dimensional systems, unpinned cases and anharmonic interactions are also considered.
Open AccessOn the Conversion of Work into Heat: Microscopic Models and Macroscopic Equations
We summarize and extend some of the results obtained recently for the microscopic and macroscopic behavior of a pinned harmonic chain, with random velocity flips at Poissonian times, acted on by a periodic force {at one end} and in contact with a heat bath at the other end. Here we consider the case where the system is in contact with two heat baths at different temperatures and a periodic force is applied at any position. This leads in the hydrodynamic limit to a heat equation for the temperature profile with a discontinuous slope at the position where the force acts. Higher dimensional systems, unpinned cases and anharmonic interactions are also considered.
- Open Access
- 14 April 2023
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 190 (4) , 1-33
Heat Flow in a Periodically Forced, Thermostatted Chain II
We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the Hamiltonian equation of motion plus a reversal of the velocity of a particle occurring independently for each particle at exponential times, with rate $$\gamma $$ . The latter produces a finite heat conductivity. Starting with an initial probability distribution for a chain of n particles we compute the current and the local temperature given by the expected value of the local energy. Scaling space and time diffusively yields, in the $$n\rightarrow +\infty $$ limit, the heat equation for the macroscopic temperature profile T(t, u), $$t>0$$ , $$u \in [0,1]$$ . It is to be solved for initial conditions T(0, u) and specified $$T(t,0)=T_-$$ , the temperature of the left heat reservoir and a fixed heat flux J, entering the system at $$u=1$$ . |J| equals the work done by the periodic force which is computed explicitly for each n.- 14 April 2023
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 190 (4) , 1-33
Open AccessHeat Flow in a Periodically Forced, Thermostatted Chain II
We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the Hamiltonian equation of motion plus a reversal of the velocity of a particle occurring independently for each particle at exponential times, with rate $$\gamma $$ . The latter produces a finite heat conductivity. Starting with an initial probability distribution for a chain of n particles we compute the current and the local temperature given by the expected value of the local energy. Scaling space and time diffusively yields, in the $$n\rightarrow +\infty $$ limit, the heat equation for the macroscopic temperature profile T(t, u), $$t>0$$ , $$u \in [0,1]$$ . It is to be solved for initial conditions T(0, u) and specified $$T(t,0)=T_-$$ , the temperature of the left heat reservoir and a fixed heat flux J, entering the system at $$u=1$$ . |J| equals the work done by the periodic force which is computed explicitly for each n. - Open Access
Heat flow in a periodically forced, thermostatted chain II
We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the Hamiltonian equation of motion plus a reversal of the velocity of a particle occurring independently for each particle at exponential times, with rate $\gamma$. The latter produces a finite heat conductivity. Starting with an initial probability distribution for a chain of $n$ particles we compute the local temperature given by the expected value of the local energy and current. Scaling space and time diffusively yields, in the $n\to+\infty$ limit, the heat equation for the macroscopic temperature profile $T(t,u),$ $t>0$, $u \in [0,1]$. It is to be solved for initial conditions $T(0,u)$ and specified $T(t,0)=T_-$, the temperature of the left heat reservoir and a fixed heat flux $J$, entering the system at $u=1$. $J$ is the work done by the periodic force which is computed explicitly for each $n$.Open AccessHeat flow in a periodically forced, thermostatted chain II
We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the Hamiltonian equation of motion plus a reversal of the velocity of a particle occurring independently for each particle at exponential times, with rate $\gamma$. The latter produces a finite heat conductivity. Starting with an initial probability distribution for a chain of $n$ particles we compute the local temperature given by the expected value of the local energy and current. Scaling space and time diffusively yields, in the $n\to+\infty$ limit, the heat equation for the macroscopic temperature profile $T(t,u),$ $t>0$, $u \in [0,1]$. It is to be solved for initial conditions $T(0,u)$ and specified $T(t,0)=T_-$, the temperature of the left heat reservoir and a fixed heat flux $J$, entering the system at $u=1$. $J$ is the work done by the periodic force which is computed explicitly for each $n$. - 8 February 2023
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 400 (3) , 2181-2225
Heat Flow in a Periodically Forced, Thermostatted Chain
- 8 February 2023
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 400 (3) , 2181-2225
Heat Flow in a Periodically Forced, Thermostatted Chain