854 research outputs found
Nonadiabatic Electron Pumping: Maximal Current with Minimal Noise
The noise properties of pump currents through an open double quantum dot
setup with non-adiabatic ac driving are investigated. Driving frequencies close
to the internal resonances of the double dot-system mark the optimal working
points at which the pump current assumes a maximum while its noise power
possesses a remarkably low minimum. A rotating-wave approximation provides
analytical expressions for the current and its noise power and allows to
optimize the noise characteristics. The analytical results are compared to
numerical results from a Floquet transport theory.Comment: 4 pages, 3 figures, replaced Fig. 1, added new inset in Fig. 2,
extended paragraph on symmetry consideration
Thermodynamics and Fluctuation Theorems for a Strongly Coupled Open Quantum System: An Exactly Solvable Case
We illustrate recent results concerning the validity of the work fluctuation
theorem in open quantum systems [M. Campisi, P. Talkner, and P. H\"{a}nggi,
Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable
model of an open quantum system. The central role played by the thermodynamic
partition function of the open quantum system, -- a two level fluctuator with a
strong quantum nondemolition coupling to a harmonic oscillator --, is
elucidated. The corresponding quantum Hamiltonian of mean force is evaluated
explicitly. We study the thermodynamic entropy and the corresponding specific
heat of this open system as a function of temperature and coupling strength and
show that both may assume negative values at nonzero low temperatures.Comment: 8 pages, 6 figure
Specific heat anomalies of open quantum systems
The evaluation of the specific heat of an open, damped quantum system is a
subtle issue. One possible route is based on the thermodynamic partition
function which is the ratio of the partition functions of system plus bath and
of the bath alone. For the free damped particle it has been shown, however,
that the ensuing specific heat may become negative for appropriately chosen
environments. Being an open system this quantity then naturally must be
interpreted as the change of the specific heat obtained as the difference
between the specific heat of the heat bath coupled to the system degrees of
freedom and the specific heat of the bath alone. While this difference may
become negative, the involved specific heats themselves are always positive;
thus, the known thermodynamic stability criteria are perfectly guaranteed. For
a damped quantum harmonic oscillator, instead of negative values, under
appropriate conditions one can observe a dip in the difference of specific
heats as a function of temperature. Stylized minimal models containing a single
oscillator heat bath are employed to elucidate the occurrence of the anomalous
temperature dependence of the corresponding specific heat values. Moreover, we
comment on the consequences for the interpretation of the density of states
based on the thermal partitionfunction.Comment: 7 pages, 6 figures, new title and some modifications of the main tex
Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems
Voltage-dependent ion channels determine the electric properties of axonal
cell membranes. They not only allow the passage of ions through the cell
membrane but also contribute to an additional charging of the cell membrane
resulting in the so-called capacitance loading. The switching of the channel
gates between an open and a closed configuration is intrinsically related to
the movement of gating charge within the cell membrane. At the beginning of an
action potential the transient gating current is opposite to the direction of
the current of sodium ions through the membrane. Therefore, the excitability is
expected to become reduced due to the influence of a gating current. Our
stochastic Hodgkin-Huxley like modeling takes into account both the channel
noise -- i.e. the fluctuations of the number of open ion channels -- and the
capacitance fluctuations that result from the dynamics of the gating charge. We
investigate the spiking dynamics of membrane patches of variable size and
analyze the statistics of the spontaneous spiking. As a main result, we find
that the gating currents yield a drastic reduction of the spontaneous spiking
rate for sufficiently large ion channel clusters. Consequently, this
demonstrates a prominent mechanism for channel noise reduction.Comment: 18 page
Directed transport in periodically rocked random sawtooth potentials
We study directed transport of overdamped particles in a periodically rocked
random sawtooth potential. Two transport regimes can be identified which are
characterized by a nonzero value of the average velocity of particles and a
zero value, respectively. The properties of directed transport in these regimes
are investigated both analytically and numerically in terms of a random
sawtooth potential and a periodically varying driving force. Precise conditions
for the occurrence of transition between these two transport regimes are
derived and analyzed in detail.Comment: 18 pages, 7 figure
Checking the validity of truncating the cumulant hierarchy description of a small system
We analyze the behavior of the first few cumulant in an array with a small
number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf
19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global
coupling and derived an infinite hierarchy of differential equations for the
cumulant moments. They focused on the behavior of infinite size systems using a
strategy based on truncating the hierarchy. In this work we explore the
reliability of such an approach to describe systems with a small number of
elements. We carry out an extensive numerical analysis of the truncated
hierarchy as well as numerical simulations of the full set of Langevin
equations governing the dynamics. We find that the results provided by the
truncated hierarchy for finite systems are at variance with those of the
Langevin simulations for large regions of parameter space. The truncation of
the hierarchy leads to a dependence on initial conditions and to the
coexistence of states which are not consistent with the theoretical
expectations based on the multidimensional linear Fokker-Planck equation for
finite arrays
Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels
In the absence of advection, confined diffusion characterizes transport in
many natural and artificial devices, such as ionic channels, zeolites, and
nanopores. While extensive theoretical and numerical studies on this subject
have produced many important predictions, experimental verifications of the
predictions are rare. Here, we experimentally measure colloidal diffusion times
in microchannels with periodically varying width and contrast results with
predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While
the theory and simulation correctly predict the entropic effect of the varying
channel width, they fail to account for hydrodynamic effects, which include
both an overall decrease and a spatial variation of diffusivity in channels.
Neglecting such hydrodynamic effects, the theory and simulation underestimate
the mean and standard deviation of first passage times by 40\% in channels with
a neck width twice the particle diameter. We further show that the validity of
the Fick-Jakobs theory can be restored by reformulating it in terms of the
experimentally measured diffusivity. Our work thus demonstrates that
hydrodynamic effects play a key role in diffusive transport through narrow
channels and should be included in theoretical and numerical models.Comment: 7 pages, 4 figure
Microcanonical quantum fluctuation theorems
Previously derived expressions for the characteristic function of work
performed on a quantum system by a classical external force are generalized to
arbitrary initial states of the considered system and to Hamiltonians with
degenerate spectra. In the particular case of microcanonical initial states
explicit expressions for the characteristic function and the corresponding
probability density of work are formulated. Their classical limit as well as
their relations to the respective canonical expressions are discussed. A
fluctuation theorem is derived that expresses the ratio of probabilities of
work for a process and its time reversal to the ratio of densities of states of
the microcanonical equilibrium systems with corresponding initial and final
Hamiltonians.From this Crooks-type fluctuation theorem a relation between
entropies of different systems can be derived which does not involve the time
reversed process. This entropy-from-work theorem provides an experimentally
accessible way to measure entropies.Comment: revised and extended versio
Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model
The influence of intrinsic channel noise on the spontaneous spiking activity
of poisoned excitable membrane patches is studied by use of a stochastic
generalization of the Hodgkin-Huxley model. Internal noise stemming from the
stochastic dynamics of individual ion channels is known to affect the
collective properties of the whole ion channel cluster. For example, there
exists an optimal size of the membrane patch for which the internal noise alone
causes a regular spontaneous generation of action potentials. In addition to
varying the size of ion channel clusters, living organisms may adapt the
densities of ion channels in order to optimally regulate the spontaneous
spiking activity. The influence of channel block on the excitability of a
membrane patch of certain size is twofold: First, a variation of ion channel
densities primarily yields a change of the conductance level. Second, a
down-regulation of working ion channels always increases the channel noise.
While the former effect dominates in the case of sodium channel block resulting
in a reduced spiking activity, the latter enhances the generation of
spontaneous action potentials in the case of a tailored potassium channel
blocking. Moreover, by blocking some portion of either potassium or sodium ion
channels, it is possible to either increase or to decrease the regularity of
the spike train.Comment: 10 pages, 3 figures, published 200
Finite quantum dissipation: the challenge of obtaining specific heat
We consider a free particle coupled with finite strength to a bath and
investigate the evaluation of its specific heat. A harmonic oscillator bath of
Drude type with cutoff frequency omega_D is employed to model an ohmic friction
force with dissipation strength gamma. Two scenarios for obtaining specific
heat are presented. The first one uses the measurement of the kinetic energy of
the free particle while the second one is based on the reduced partition
function. Both descriptions yield results which are consistent with the Third
Law of thermodynamics. Nevertheless, the two methods produce different results
that disagree even in their leading quantum corrections at high temperatures.
We also consider the regime where the cutoff frequency is smaller than the
friction strength, i.e. omega_D<gamma. There, we encounter puzzling results at
low temperatures where the specific heat based on the thermodynamic
prescription becomes negative. This anomaly is rooted in an ill-defined density
of states of the damped free particle which assumes unphysical negative values
when gamma/omega_D>1.Comment: 16 pages, 4 figure
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