NOISE AND CORRELATED TRANSPORT IN ION CHANNELS

2004 ◽  
Vol 04 (01) ◽  
pp. L171-L178 ◽  
Author(s):  
H. HAKEN
Keyword(s):  
Occupation Number ◽  
Rate Equations ◽  
Quantum Mechanical ◽  
Transition Rates ◽  
Operator Equations ◽  
Occupation Numbers ◽  
Classical Quantum ◽  
The Individual ◽  
Quantum Mechanical Operator ◽  
Mechanical Operator

The motion of an ion through a channel is described as a classical/quantum mechanical hopping process between the individual sites of a channel. The transition rates are due to the coupling of an ion to suitable reservoirs. If fluctuating forces are added to the rate equations for the occupation numbers, the equations become quantum mechanical operator equations. Using previous results, the fluctuating forces are uniquely determined by the requirement of quantum mechanical consistency. The resulting equations are solved for several cases and the occupation number fluctuations discussed. Particular emphasis is laid on a model of correlated transport.

scholarly journals On the Spectrum of the Local $${\mathbb {P}}^2$$ Mirror Curve

2020 ◽  
Vol 21 (11) ◽  
pp. 3479-3497
Author(s):  
Rinat Kashaev ◽  
Sergey Sergeev
Keyword(s):  
Spectral Problem ◽  
Bethe Ansatz ◽  
Quantum Mechanical ◽  
Planck’S Constant ◽  
Transcendental Equations ◽  
Del Pezzo ◽  
Planck's Constant ◽  
Quantum Mechanical Operator ◽  
Mechanical Operator

Abstract We address the spectral problem of the formally normal quantum mechanical operator associated with the quantised mirror curve of the toric (almost) del Pezzo Calabi–Yau threefold called local $${\mathbb {P}}^2$$ P 2 in the case of complex values of Planck’s constant. We show that the problem can be approached in terms of the Bethe ansatz-type highly transcendental equations.

DIRECTED MOTION OF BROWNIAN MOTORS: A RATCHET MODEL OF TWO-COUPLED MOLECULAR MOTORS

2007 ◽  
Vol 21 (28) ◽  
pp. 1915-1921 ◽  
Author(s):  
SHUTANG WEN ◽  
HONGWEI ZHANG ◽  
LEIAN LIU ◽  
XIAOFENG SUN ◽  
YUXIAO LI
Keyword(s):  
Molecular Motors ◽  
Particle System ◽  
Langevin Equations ◽  
Transition Rates ◽  
Neck Length ◽  
Directed Motion ◽  
Mean Velocity ◽  
Positive Direction ◽  
Brownian Motors ◽  
The Individual

We investigated the motion of two-head Brownian motors by introducing a model in which the two heads coupled through an elastic spring is subjected to a stochastic flashing potential. The ratchet potential felt by the individual head is anti-correlated. The mean velocity was calculated based on Langevin equations. It turns out that we can obtain a unidirectional current. The current is sensitive to the transition rates and neck length and other parameters. The coupling of transition rate and neck length leads to variations both in the values and directions of currency. With a larger neck length, the bi-particle system has a larger velocity in one direction, while with a smaller neck length, it has a smaller velocity in the other direction. This is very likely the case of myosins with a larger neck length and larger velocity in the positive direction of filaments and kinesins with a smaller neck length and smaller velocity in the negative direction of microtubules. We also further investigated how current reversal depended on the neck length and the transition rates.

A LINEAR CORRELATION OF PROTON CHEMICAL SHIFTS IN SOME ALKYL CHLORIDES AND HYDROCARBONS WITH THE OCCUPATION NUMBER OF THE HYDROGEN ORBITALS

1965 ◽  
Vol 43 (12) ◽  
pp. 3188-3192 ◽  
Author(s):  
F. Hruska ◽  
G. Kotowycz ◽  
T. Schaefer
Keyword(s):  
Linear Correlation ◽  
Occupation Number ◽  
Chemical Shifts ◽  
The Self ◽  
Starting Values ◽  
Occupation Numbers ◽  
Self Consistent ◽  
Consistent Group ◽  
Proton Chemical Shifts ◽  
Group Orbital

A linear correlation exists between the proton shifts of some alkyl chlorides and some hydrocarbons and the occupation numbers of the hydrogen 1s orbitals in the C—H bonds. The occupation numbers are those given by the self-consistent group orbital and bond electronegativity method. The application of this correlation to the prediction of starting values for occupation numbers, to the derivation of bond anisotropies in ethylene and acetylene, and to the prediction of hydrogen-bonded shifts of C—H protons is discussed.

THE PAULI PRINCIPLE AND QUANTUM TRANSPORT

1994 ◽  
Vol 08 (21n22) ◽  
pp. 1377-1385 ◽  
Author(s):  
S.A. GURVITZ ◽  
H.J. LIPKIN ◽  
Ya. S. PRAGER
Keyword(s):  
Quantum Wells ◽  
Resonant Tunneling ◽  
Fock Space ◽  
Pauli Principle ◽  
Semiconductor Heterostructures ◽  
Rate Equations ◽  
Semiconductor Quantum Wells ◽  
Occupation Numbers ◽  
The One ◽  
Space Wave

A new method using Fock space wave functions is proposed for studying resonant tunneling in semiconductor quantum wells. The use of binary occupation numbers as dynamical variables, rather than properties of individual electrons, manifestly takes account of electron statistics, which enables investigation of the influence of the Pauli principle on resonant tunneling in the presence of inelastic scattering. Applied to the evaluation of the resonant current in semiconductor heterostructures, our approach predicts considerable deviations from the one-electron and rate equations pictures.

The quantum mechanical theory of environmental effects

1960 ◽  
Vol 255 (1280) ◽  
pp. 63-68 ◽  
Keyword(s):  
Wave Function ◽  
Environmental Effects ◽  
Quantum Mechanical ◽  
Mechanical Theory ◽  
Wave Mechanics ◽  
Quantum Mechanical Theory ◽  
The Individual

A basic postulate of wave mechanics is that the wave function of a microscopic system develops in time according to the equation iℏ∂ψ/∂ t = H ψ, where H , the Hamiltonian, is an operator which in general depends upon the time. If, and only if, the Hamiltonian is time-independent, then the solutions of this equation take the form ψ( q, t ) = ∑ n c n Ѱ n ( q )e -1 E n t /ℏ , (2) where the individual terms Ѱ n ( q ) are functions of the co-ordinates alone and the E n are the corresponding eigenvalues of the Hamiltonian, satisfying HѰ n = E n Ѱ n . (3)

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