Stochastic Simulation of a Casimir Oscillator

2010 ◽  
Author(s):  
Farbod Khoshnoud ◽  
Houman Owhadi ◽  
Clarence W. de Silva
Keyword(s):  
Stochastic Simulation ◽  
Casimir Force ◽  
Casimir Effect ◽  
Zero Point ◽  
Realistic Model ◽  
Sensors And Actuators ◽  
Moving Plate ◽  
Fixed Plate ◽  
Analysis And Design ◽  
Spring Force

Stochastic simulation of a Casimir Oscillator is presented in this paper. This oscillator is composed of a flat boundary of semiconducting oscillator parallel to a fixed plate separated by vacuum. In this system the oscillating surface is attracted to the fixed plate by the Casimir effect, due to quantum fluctuations in the zero point electromagnetic field. Motion of the oscillating boundary is opposed by a spring. The stored potential energy in the spring is converted into kinetic energy when the spring force exceeds the Casimir force, which generates an oscillatory motion of the moving plate. Casimir Oscillators are used as micro-mechanical switches, sensors and actuators. In the present paper, a stochastic simulation of a Casimir oscillator is presented for the first time. In this simulation, Stochastic Variational Integrators using a Langevin equation, which describes Brownian motion, is considered. Formulations for Symplectic Euler, Constrained Symplectic Euler, Stormer-Verlet and RATTLE integrators are obtained and the Symplectic Euler case is solved numerically. When the moving parts in a micro/nano system travel in the vicinity of 10 nanometers to 1 micrometer range relative to other parts of the system, the Casimir phenomenon is in effect and should be considered in analysis and design of such system. The simulation in this paper considers modeling such uncertainties as friction, effect of surface roughness on the Casimir force, and change in environmental conditions such as ambient temperature. In this manner the paper explores a realistic model of the Casimir Oscillator. Furthermore, the presented study of this system provides a deeper understanding of the nature of the Casimir force.

CASIMIR FORCE BETWEEN A GRAVITATIONAL FIELD AND A FINITE OBJECT

2002 ◽  
Vol 11 (10) ◽  
pp. 1567-1572 ◽  
Author(s):  
FABRIZIO PINTO
Keyword(s):  
Gravitational Field ◽  
Casimir Force ◽  
Casimir Effect ◽  
Finite Size ◽  
Zero Point ◽  
Point Energy ◽  
Energy Field ◽  
Static Gravitational Field ◽  
Vacuum Gap ◽  
Infinite Media

In the typical Casimir effect, the boundaries of two semi-infinite media exert a force upon one another across a vacuum gap separating them. In this paper, I argue that a static gravitational field can be regarded as a "soft" boundary which interacts with a test object of finite size through the electromagnetic zero-point-energy field. Therefore, a pressure exists upon a single slab placed in a gravitational field and surrounded by a vacuum. Interestingly, this extremely small Casimir pressure of the gravitational field may cause relative displacements in ground-based sensing microstructures larger than those from astrophysical gravitational waves in macroscopic antennas.

On Convergence Generation in Computing the Electro-Magnetic Casimir Force

2008 ◽  
Vol 63 (9) ◽  
pp. 571-574
Author(s):  
Frédéric Schuller
Keyword(s):  
Casimir Force ◽  
Fundamental Problem ◽  
Casimir Effect ◽  
Zero Point ◽  
Zero Point Energy ◽  
Point Energy ◽  
Cavity Radiation ◽  
Field Fluctuations ◽  
Electro Magnetic

We tackle the very fundamental problem of zero-point energy divergence in the context of the Casimir effect. We calculate the Casimir force due to field fluctuations by using standard cavity radiation modes. The validity of convergence generation by means of an exponential energy cut-off factor is discussed in detail.

Analysis and Design of a Nano-Electromechanical Vibration Sensor

2010 ◽  
Author(s):  
Farbod Khoshnoud ◽  
Clarence W. de Silva ◽  
Houman Owhadi
Keyword(s):  
Carbon Nanotube ◽  
Casimir Effect ◽  
Zero Point ◽  
Capacitive Sensor ◽  
Structural Condition ◽  
Vibration Sensor ◽  
Vibration Monitoring ◽  
Vibration Measurement ◽  
Element Analysis ◽  
Analysis And Design

Design and analysis of an embedded nano-electromechanical capacitive sensor for vibration monitoring is presented in this paper. In this sensor, vibration sensing is carried out by detecting the oscillations of a Single Walled Carbon Nanotube (SWCNT). The SWCNT is excited when it is subjected to a base motion corresponding to the measured vibration. Acquisition of the sensor signal is performed by a capacitance circuit, using the electric charge generated in the Carbon Nanotube (CNT). A modulation in the charge in the CNT, due to change in the capacitance, leads to a modulation in the CNT’s conductance and is used in measuring the input vibration. Vibration properties of the CNTs are obtained by molecular mechanics and finite element analysis where atoms are modeled as particles with an equilibrium distance equal to the bond length, and the bonded interactions of atoms are modeled as flexible beams. Stiffness coefficients of the atomic bonds are modeled using Morse atomic potential. A bridge circuit is utilized in this sensor to compensate for temperature and other environmental effects. When the CNT is in the vicinity of the gate underneath the tube, at a distance in the range of 1 nanometer to 1 micrometer, Casimir pressure, due to quantum fluctuations in the zero point electromagnetic field, can attract the CNT to the gate. This unwanted applied force on the tube may lead to inaccurate measurement of the vibration. In order to study the effect of Casimir pressure on the CNT a simplified model of the Casimir effect, for parallel surfaces, is adopted. This model can assist in achieving better accuracy in vibration measurement, and the sensor can be calibrated accordingly to account for the Casimir attractive force. The paper presents the physical and operational details of the sensor. This device is particularly useful for precise and effective sensing of vibration for machinery and structural condition monitoring and fault diagnosis.

scholarly journals NEW CONSTRAINTS ON YUKAWA-TYPE INTERACTIONS FROM THE CASIMIR EFFECT

2012 ◽  
Vol 14 ◽  
pp. 200-214
Author(s):  
V. M. MOSTEPANENKO ◽  
V. B. BEZERRA ◽  
G. L. KLIMCHITSKAYA ◽  
C. ROMERO
Keyword(s):  
Standard Model ◽  
Casimir Force ◽  
Casimir Effect ◽  
Beyond The Standard Model ◽  
Exact Theory ◽  
The Standard Model

Measurements of the Casimir force are used to obtain stronger constraints on the parameters of hypothetical interactions predicted in different unification schemes beyond the Standard Model. We review new strong constraints on the Yukawa-type interactions derived during the last two years from recent experiments on measuring the lateral Casimir force, Casimir force in configurations with corrugated boundaries and the Casimir-Polder force. Specifically, from measurements of the lateral Casimir force compared with the exact theory the strengthening of constraints up to a factor of 24 millions was achieved. We also discuss further possibilities to strengthen constraints on the Yukawa interactions from the Casimir effect.

A new approach to detecting gravitational waves via the coupling of gravity to the zero-point energy of the phonon modes of a superconductor

2017 ◽  
Vol 26 (12) ◽  
pp. 1743031 ◽  
Author(s):  
Nader A. Inan
Keyword(s):  
Gravitational Wave ◽  
Casimir Effect ◽  
Zero Point ◽  
Harmonic Oscillators ◽  
Phonon Modes ◽  
Zero Point Energy ◽  
Dynamical Casimir Effect ◽  
Point Energy ◽  
Pair Density ◽  
Ionic Lattice

The response of a superconductor to a gravitational wave is shown to obey a London-like constituent equation. The Cooper pairs are described by the Ginzburg–Landau free energy density embedded in curved spacetime. The lattice ions are modeled by quantum harmonic oscillators characterized by quasi-energy eigenvalues. This formulation is shown to predict a dynamical Casimir effect since the zero-point energy of the ionic lattice phonons is modulated by the gravitational wave. It is also shown that the response to a gravitational wave is far less for the Cooper pair density than for the ionic lattice. This predicts a “charge separation effect” which can be used to detect the passage of a gravitational wave.

Remarks on the vacuum energy in interacting scalar field theory

1990 ◽  
Vol 68 (1) ◽  
pp. 91-95 ◽  
Author(s):  
T. F. Treml
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Path Integral ◽  
Vacuum Energy ◽  
Casimir Effect ◽  
Dimensional Regularization ◽  
Zero Point ◽  
Scalar Field Theory ◽  
Method Of Calculation ◽  
Independent Term

The vacuum energy in interacting scalar field theory is computed in the case of the Casimir effect as a sum over zero-point energies and as a path-integral determinant, using both ζ-function regularization and dimensional regularization. Using a simple nonrecursive method of calculation, the two forms of the vacuum energy are shown to differ before renormalization by a scale-independent term when ζ-function regularization is used, but yield exactly the same result when dimensional regularization is used.

scholarly journals The Casimir effect for thick pistons

2016 ◽  
Vol 31 (06) ◽  
pp. 1650012
Author(s):  
Guglielmo Fucci
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Regularization Method ◽  
Casimir Force ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Numerical Results ◽  
Spectral Zeta Function

In this work, we analyze the Casimir energy and force for a thick piston configuration. This study is performed by utilizing the spectral zeta function regularization method. The results we obtain for the Casimir energy and force depend explicitly on the parameters that describe the general self-adjoint boundary conditions imposed. Numerical results for the Casimir force are provided for specific types of boundary conditions and are also compared to the corresponding force on an infinitely thin piston.

scholarly journals ON THE CASIMIR EFFECT FOR PARALLEL PLATES IN THE SPACETIME WITH ONE EXTRA COMPACTIFIED DIMENSION

2006 ◽  
Vol 21 (25) ◽  
pp. 1957-1963 ◽  
Author(s):  
HONGBO CHENG
Keyword(s):  
Extra Dimension ◽  
Casimir Force ◽  
Casimir Effect ◽  
Universal Extra Dimension ◽  
Parallel Plates

In this paper, the Casimir effect for parallel plates in the presence of one compactified universal extra dimension is re-examined in detail. Having regularized the expressions of Casimir force, we show that the nature of Casimir force is repulsive if the distance between the plates is large enough, which does not agree with the experimental phenomena.

scholarly journals Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Sébastien Léger ◽  
Javier Puertas-Martínez ◽  
Karthik Bharadwaj ◽  
Rémy Dassonneville ◽  
Jovian Delaforce ◽  
...  
Keyword(s):  
Casimir Effect ◽  
Structure Constant ◽  
Zero Point ◽  
Fine Structure Constant ◽  
Many Body ◽  
Bloch Oscillations ◽  
Superconducting Circuits ◽  
High Impedance ◽  
Non Linear ◽  
Large Phase

AbstractElectromagnetic fields possess zero point fluctuations which lead to observable effects such as the Lamb shift and the Casimir effect. In the traditional quantum optics domain, these corrections remain perturbative due to the smallness of the fine structure constant. To provide a direct observation of non-perturbative effects driven by zero point fluctuations in an open quantum system we wire a highly non-linear Josephson junction to a high impedance transmission line, allowing large phase fluctuations across the junction. Consequently, the resonance of the former acquires a relative frequency shift that is orders of magnitude larger than for natural atoms. Detailed modeling confirms that this renormalization is non-linear and quantum. Remarkably, the junction transfers its non-linearity to about thirty environmental modes, a striking back-action effect that transcends the standard Caldeira-Leggett paradigm. This work opens many exciting prospects for longstanding quests such as the tailoring of many-body Hamiltonians in the strongly non-linear regime, the observation of Bloch oscillations, or the development of high-impedance qubits.

Chern-Simons boundary layers in the Casimir effect

2020 ◽  
Vol 35 (03) ◽  
pp. 2040015 ◽  
Author(s):  
Valery N. Marachevsky
Keyword(s):  
Boundary Layers ◽  
Casimir Force ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Energy Minimum ◽  
Strong Reduction ◽  
Si Substrates ◽  
Glass Substrates ◽  
Chern Simons ◽  
Substrate Influence

Casimir interaction of two SiO2 glass half spaces being substrates for Chern-Simons boundary layers is studied. The separation between two half spaces at which the Casimir energy minimum occurs is strongly increased for dielectric SiO2 glass substrates in comparison with previously considered metal Au and semiconductor Si substrates. Strong reduction in the Casimir force due to presence of Chern-Simons layers is found for SiO2 glass substrate. Influence of modification of the infrared absorption on the Casimir force is studied.

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