Escape of particles in a time-dependent potential well.

We investigate the escape of an ensemble of noninteracting particles inside an infinite potential box that contains a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear area-preserving mapping for the variables energy and time, leading to a mixed phase space. The chaotic sea in the phase space surrounds periodic islands and is limited by a set of invariant spanning curves. When a hole is introduced in the energy axis, the histogram of frequency for the escape of particles, which we observe to be scaling invariant, grows rapidly until it reaches a maximum and then decreases toward zero at sufficiently long times. A plot of the survival probability of a particle in the dynamics as function of time is observed to be exponential for short times, reaching a crossover time and turning to a slower-decay regime, due to sticky regions observed in the phase space.

[1]  J. Mateos,et al.  Traversal-time distribution for a classical time-modulated barrier , 1999 .

[2]  George M. Zaslavsky,et al.  Physics of Chaos in Hamiltonian Systems , 1998 .

[3]  C. Dettmann,et al.  Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates , 2006, nlin/0610013.

[4]  G. A. Luna-Acosta,et al.  Chaotic classical scattering and dynamics in oscillating 1-D potential wells , 2001 .

[5]  E. Leonel,et al.  Dynamical properties of a particle in a classical time-dependent potential well , 2003 .

[6]  G. Zaslavsky.  Chaos, fractional kinetics, and anomalous transport , 2002 .

[7]  G. Cristadoro,et al.  Universality of algebraic decays in Hamiltonian systems. , 2008, Physical review letters.

[8]  Traversal Time for Tunneling , 1982 .

[9]  Kouwenhoven,et al.  Transport through a finite one-dimensional crystal. , 1990, Physical review letters.

[10]  P. McClintock,et al.  Dynamical properties of a particle in a time-dependent double-well potential , 2004 .

[11]  E. Altmann,et al.  Poincaré recurrences and transient chaos in systems with leaks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  H. Kantz,et al.  Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  P. McEuen,et al.  Observation of photon-assisted tunneling through a quantum dot. , 1994, Physical review letters.

[14]  E. Leonel,et al.  Finding critical exponents for two-dimensional Hamiltonian maps. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  C. Manchein,et al.  Gauss map and Lyapunov exponents of interacting particles in a billiard , 2009, 0903.0177.

[16]  A. d’Onofrio.  Fractal growth of tumors and other cellular populations: Linking the mechanistic to the phenomenological modeling and vice versa , 2009, 1309.3329.

[17]  J. V. José,et al.  Energy transfer of a chaotic particle in a classical oscillating potential barrier , 1998 .

[18]  V. Constantoudis,et al.  Classical scattering from oscillating targets , 2002 .

[19]  V. Constantoudis,et al.  Scattering off two oscillating disks: dilute chaos. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  R. Hwang.  Negative group velocity and anomalous transmission in a one-dimensionally periodic waveguide , 2006 .

[21]  Nonperiodic delay mechanism and fractallike behavior in classical time-dependent scattering. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  P. McClintock,et al.  Chaotic properties of a time-modulated barrier. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  T. Seligman,et al.  The chaotic set and the cross section for chaotic scattering in three degrees of freedom , 2010, 1004.1124.

[24]  Eduardo G Altmann,et al.  Recurrence time statistics for finite size intervals. , 2004, Chaos.

[25]  Lent,et al.  Recovery of quantized ballistic conductance in a periodically modulated channel. , 1993, Physical review letters.

[26]  Carles Simó,et al.  Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps , 2009 .

[27]  C. Simó,et al.  Dynamics in chaotic zones of area preserving maps: Close to separatrix and global instability zones , 2011 .

[28]  H. Buljan,et al.  Many-hole interactions and the average lifetimes of chaotic transients that precede controlled periodic motion. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Hopkins,et al.  Photon-mediated sequential resonant tunneling in intense terahertz electric fields. , 1993, Physical review letters.

[30]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[31]  Multiple components in narrow planetary rings. , 2007, Physical review letters.

[32]  LETTER TO THE EDITOR: Stochastic resonance in a bistable piecewise potential: analytical solution , 1996 .

[33]  Oded Farago,et al.  Directed chaotic motion in a periodic potential , 1998 .

[34]  P. McClintock,et al.  Scaling properties for a classical particle in a time-dependent potential well. , 2005, Chaos.