arXiv subjects

G. W. Ford

Publications and source records attributed to G. W. Ford.

At least 19 recordsLinked to original sources

arXiv2014

A pair of oscillators interacting with a common heat bath

Here the problem considered is that of a pair of oscillators coupled to a common heat bath. Many, if not most, discussions of a single operator coupled to a bath have used the independent oscillator model of the bath. However, that model has no notion of separation, so the question of phenomena when the oscillators are near one another compared with when they are widely separated cannot be addressed. Here the Lamb model of an oscillator attached to a stretched string is generalized to illustrate some of these questions. The coupled Langevin equations for a pair of oscillators attached to the string at different points are derived and their limits for large and small separations obtained. Finally, as an illustration of a different phenomenon, the fluctuation force between a pair of masses attached to the string is calculated, with closed form expressions for the force at small and large separations.

quant-ph↗

arXiv2013

Lorentz Transformation of Blackbody Radiation

We present a simple calculation of the Lorentz transformation of the spectral distribution of blackbody radiation at temperature T. Here we emphasize that T is the temperature in the blackbody rest frame and does not change. We thus avoid the confused and confusing question of how temperature transforms. We show by explicit calculation that at zero temperature the spectral distribution is invariant. At finite temperature we find the well known result familiar in discussions of the the 2.7! K cosmic radiation.

quant-ph↗

arXiv2011

Consistency of a Causal Theory of Radiative Reaction with the Optical Theorem

The Abraham-Lorentz-Dirac equation for a point electron, while suffering from runaway solutions and an acausal response to external forces, is compatible with the optical theorem. We show that a theory of radiative reaction that allows for a finite charge distribution is not only causal and free of runaway solutions, but is also consistent with the optical theorem and the standard formula for the Rayleigh scattering cross section.

quant-ph↗

arXiv2010

Disentanglement and Decoherence without dissipation at non-zero temperatures

Decoherence is well understood, in contrast to disentanglement. According to common lore, irreversible coupling to a dissipative environment is the mechanism for loss of entanglement. Here, we show that, on the contrary, disentanglement can in fact occur at large enough temperatures $T$ even for vanishingly small dissipation (as we have shown previously for decoherence). However, whereas the effect of $T$ on decoherence increases exponentially with time, the effect of $T$ on disentanglement is constant for all times, reflecting a fundamental difference between the two phenomena. Also, the possibility of disentanglement at a particular $T$ increases with decreasing initial entanglement.

quant-ph↗

arXiv2010

Exact analysis of disentanglement for continuous variable systems and application to a two-body system at zero temperature in an arbitrary heat bath

We outline an exact approach to decoherence and entanglement problems for continuous variable systems. The method is based on a construction of quantum distribution functions introduced by Ford and Lewis \cite{ford86} in which a system in thermal equilibrium is placed in an initial state by a measurement and then sampled by subsequent measurements. With the Langevin equation describing quantum Brownian motion, this method has proved to be a powerful tool for discussing such problems. After reviewing our previous work on decoherence and our recent work on disentanglement, we apply the method to the problem of a pair of particles in a correlated Gaussian state. The initial state and its time development are explicitly exhibited. For a single relaxation time bath at zero temperature exact numerical results are given. The criterion of Duan et al. \cite{duan00} for such states is used to prove that the state is initially entangled and becomes separable after a finite time (entanglement sudden death).

quant-ph↗

arXiv2010

Decay of Coherence and Entanglement of a Superposition State for a Continuous Variable System in an Arbitrary Heat Bath

We consider the case of a pair of particles initially in a superposition state corresponding to a separated pair of wave packets. We calculate \emph{exactly} the time development of this non-Gaussian state due to interaction with an \emph{arbitrary} heat bath. We find that coherence decays continuously, as expected. We then investigate entanglement and find that at a finite time the system becomes separable (not entangled). Thus, we see that entanglement sudden death is also prevalent in continuous variable systems which should raise concern for the designers of entangled systems.

quant-ph↗

arXiv2010

Entanglement without Dissipation: A Touchstone for an exact Comparison of Entanglement Measures

Entanglement, which is an essential characteristic of quantum mechanics, is the key element in potential practical quantum information and quantum communication systems. However, there are many open and fundamental questions (relating to entanglement measures, sudden death, etc.) that require a deeper understanding. Thus, we are motivated to investigate a simple but non-trivial correlated two-body continuous variable system in the absence of a heat bath, which facilitates an \underline{exact} measure of the entanglement at all times. In particular, we find that the results obtained from all well-known existing entanglement measures agree with each other but that, in practice, some are more straightforward to use than others.

quant-ph↗

arXiv2007

Measured quantum probability distribution functions for Brownian motion

The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle entangled with a heat bath.

quant-ph↗

arXiv2007

Quantum thermodynamic functions for an oscillator coupled to a heat bath

Small systems (of interest in the areas of nanophysics, quantum information, etc.) are particularly vulnerable to environmental effects. Thus, we determine various thermodynamic functions for an oscillator in an arbitrary heat bath at arbitrary temperatures. Explicit results are presented for the most commonly discussed heat bath models: Ohmic, single relaxation time and blackbody radiation.

quant-ph↗

arXiv2006

Anomalous diffusion in quantum Brownian motion with colored noise

Anomalous diffusion is discussed in the context of quantum Brownian motion with colored noise. It is shown that earlier results follow simply and directly from the fluctuation-dissipation theorem. The limits on the long-time dependence of anomalous diffusion are shown to be a consequence of the second law of thermodynamics. The special case of an electron interacting with the radiation field is discussed in detail. We apply our results to wave-packet spreading.

quant-ph↗

arXiv2006

A quantum violation of the second law?

An apparent violation of the second law of thermodynamics occurs when an atom coupled to a zero-temperature bath, being necessarily in an excited state, is used to extract work from the bath. Here the fallacy is that it takes work to couple the atom to the bath and this work must exceed that obtained from the atom. For the example of an oscillator coupled to a bath described by the single relaxation time model, the mean oscillator energy and the minimum work required to couple the oscillator to the bath are both calculated explicitly and in closed form. It is shown that the minimum work always exceeds the mean oscillator energy, so there is no violation of the second law.

quant-ph↗

arXiv2006

Entropy of a Quantum Oscillator coupled to a Heat Bath and implications for Quantum Thermodynamics

The free energy of a quantum oscillator in an arbitrary heat bath at a temperature T is given by a "remarkable formula" which involves only a single integral. This leads to a corresponding simple result for the entropy. The low temperature limit is examined in detail and we obtain explicit results both for the case of an Ohmic heat bath and a radiation heat bath. More general heat bath models are also examined. This enables us to determine the entropy at zero temperature in order to check the third law of thermodynamics in the quantum regime

quant-ph↗

arXiv2005

Is there Unruh radiation?

It is generally accepted that a system undergoing uniform acceleration with respect to zero-temperature vacuum will thermalize at a finite temperature (the so-called Unruh temperature) that is proportional to the acceleration. However, the question of whether or not the system actually radiates is highly controversial. Thus, we are motivated to present an exact calculation using a generalized quantum Langevin equation to describe an oscillator (the detector) moving under a constant force and coupled to a one-dimensional scalar field (scalar electrodynamics). Moreover, our analysis is simplified by using the oscillator as a detector. We show that this system does not radiate despite the fact that it does in fact thermalize at the Unruh temperature. We remark upon a differing opinion expressed regarding a system coupled to the electromagnetic field.

quant-ph↗

arXiv2005

Limitations on the Utility of Exact Master Equations

The low temperature solution of the exact master equation for an oscillator coupled to a linear passive heat bath is known to give rise to serious divergences. We now show that, even in the high temperature regime, problems also exist, notably the fact that the density matrix is not necessarily positive.

quant-ph↗

arXiv2004

Wigner Distribution Analysis of a Schrodinger Cat Superposition of Displaced Equilibrium Coherent States

Motivated by recent experiments, we consider a Schrödinger cat superposition of two widely separated coherent states in thermal equilibrium. The time development of our system is obtained using Wigner distribution functions. In contrast to our discussion for a two-Gaussian wave packet [Phys. Lett. A 286 (2001) 87], we find that, in the absence of dissipation, the interference term does not decay rapidly in time, but in common with the other two terms, it oscillates in time and persists for all times

quant-ph↗

arXiv2004

Reply to Comment on "Quantum Measurement and Decoherence"

While agreeing with our exact expression for the time dependence of the motion of a free particle in an initial superposition state, corresponding to two identical Gaussians separated by a distance $d$, at temperature $T$, Gobert et al., in the preceding Comment [Phys. Rev. A xxx], dispute our conclusions on decoherence time scales. However, the parameters they used to generate their figures are outside the regime of validity of our interpretation of the results and, moreover, are not of physical interest in that they correspond to $T\approx 0$. The point is that in their figures they have chosen the thermal de Broglie wavelength $λ_{th}=\hbar \sqrt{mkT}$ to be equal to slit spacing \emph{d}, whereas we have clearly stated [in the paragraph preceding Eq. (21) of our paper] that decoherence occurs and that our expression for the decoherence time applies only in the limit where \emph{d} is large compared not only with the slit width $σ$ but also with the thermal de Broglie wavelength, $d\gg λ_{th},σ$.

quant-ph↗

arXiv2004

Propagation of optical excitations by dipolar interactions in metal nanoparticle chains

Dispersion relations for dipolar modes propagating along a chain of metal nanoparticles are calculated by solving the full Maxwell equations, including radiation damping. The nanoparticles are treated as point dipoles, which means the results are valid only for a/d <= 1/3, where a is the particle radius and d the spacing. The discrete modes for a finite chain are first calculated, then these are mapped onto the dispersion relations appropriate for the infinite chain. Computed results are given for a chain of 50-nm diameter Ag spheres spaced by 75 nm. We find large deviations from previous quasistatic results: Transverse modes interact strongly with the light line. Longitudinal modes develop a bandwidth more than twice as large, resulting in a group velocity that is more than doubled. All modes for which k_mode <= w/c show strongly enhanced decay due to radiation damping.

physics.optics↗

arXiv2003

Decoherence at zero temperature

Most discussions of decoherence in the literature consider the high-temperature regime but it is also known that, in the presence of dissipation, decoherence can occur even at zero temperature. Whereas most previous investigations all assumed initial decoupling of the quantum system and bath, we consider that the system and environment are entangled at all times. Here, we discuss decoherence for a free particle in an initial Schrödinger cat state. Memory effects are incorporated by use of the single relaxation time model (since the oft-used Ohmic model does not give physically correct results).

quant-ph↗