Macroscopic measurement of noncommutating quantum variables

The macroscopic observer is usually concerned not with one variable, but some set of variables, the operators for which as a rule do not commutate with one another. The question then arises of what and how one must measure to obtain the most information possible about the variables being studied. A natural criterion to specify the completeness of this data is the information criterion, defining the quality of the evaluation of the given set of variables. The present study will construct a formal equivalent of an instrument optimized with regard to the information criterion for simultaneous measurement of the specified set of noncommutating quantum variables.     

The elimination of fast variables in complex chemical reactions. I. Macroscopic level

The kinetics of complex chemical reactions is considered. Different time scales exist if one or more of the rate constants of the individual reaction steps is much larger than the others. Examples of specific reactions are given in which the intermediates vary on the fast time scale. They can be eliminated according to a standard scheme, the lowest order of which coincides with the steady-state approximation usually employed in textbooks on chemical kinetics.     

Macroscopic retrocausation

Referring to Stapp's and Schmidt's recent papers: a Feynman transition amplitude |I><M><F| used retrodictively with post-selected outgoing bras<F| formalizes psychokinesis—Jaynes' qualification of the mind-induced-quantum-collapse concept. Time extendedness of matter, final cause, information-negentropy reversibility, are features inherent in relativistic quantum mechanics.     

Macroscopic chirality of strings

The macroscopic chirality of strings in xerogel obtained from a solution of N-trifluoroacetyl-R(+)-valinol in cyclohexane was revealed by atomic force microscopy and circular dichroism. The characteristic plots on different scales are reported, namely, large-scale “chaos” (∼100 μm), string commutation (∼10 μm), and “fine” structure (∼1 μm).     

Macroscopic excitations in superconductors

The dynamical density functional theory (DDFT) as an alternative approach to the mode coupling theory (MCT) for supercooled liquids and glass transitions was recast in the path integral form, which can then be analyzed by the methods of equilibrium statistical mechanics. The hope is to avoid drastic approximations entering the original MCT such as factorization of the multiparticle correlation function. The renormalized perturbation theory is developed and the freezing is interpreted as a result of the life-time renormalization. The multicomponent extension of the theory is proposed, which could be treated exactly in the limit of infinite number of the components.     

Macroscopic and microscopic reversibility

The interrelations between (1) the fluctuation-dissipation theorem in conjunction with microscopic reversibility, (2) two principles of macroscopic reversibility, (3) the Casimir-Onsager reciprocal relations, and (4) a macroscopic reciprocity theorem are investigated.     

Macroscopic and mesoscopic matter waves

It has been shown earlier [3,6] that matter waves which are known to lie typically in the range of a few angstrom, can also manifest in the macrodomain with a wave length of a few centimeters, for electrons propagating along a magnetic field. This followed from the predictions of a probability amplitude theory by the author [1,2] in the classical macrodomain of the dynamics of charged particles in a magnetic field. It is shown in this paper that this case constitutes only a special case of a generic situation whereby composite systems such as atoms and molecules in their highly excited internal states, can exhibit matter wave manifestation in macro and mesodomains, in one-dimensional scattering. The wave length of these waves is determined, not by the mass of the particle as in the case of the de Broglie wave, but by the frequency ω, of the classical orbital motion of the internal state in the correspondence limit, and is given by a nonquantal expression, λ = 2πv/ω, v being the velocity of the particle. For the electrons in a magnetic field the frequency corresponds to the gyrofrequency, Ω and the nonquantal wave length is given by λ = 2πv _|| /Ω; v _|| being the velocity of electrons along the magnetic field. Received 29 September 2001 / Received in final form 23 May 2002 Published online 19 July 2002     

Macroscopic model of plasma accelerator

A simple macroscopic model of plasma accelerator, well describing the process of the plasma cluster acceleration in the accelerator and being directly derived from the physical principles of activity of the accelerator performance, is presented in the present paper.     

Macroscopic entanglement by entanglement swapping

We present a scheme for entangling two micromechanical oscillators. The scheme exploits the quantum effects of radiation pressure and it is based on a novel application of entanglement swapping, where standard optical measurements are used to generate purely mechanical entanglement. The scheme is presented by first solving the general problem of entanglement swapping between arbitrary bipartite Gaussian states, for which simple input-output formulas are provided.     

Macroscopic magnetic fields of antiferromagnets

The macroscopic magnetic fields arising in the space outside or in the bulk of an antiferromagnet in the absence of external currents are a result of surface magnetization. The general problem of determining these fields is formulated. It is shown that the field distribution near special lines on the surface is monopolar. An experimental study of the field makes it possible to determine the surface magnetization on the faces of an antiferromagnetic crystal. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 724–728 (10 May 1996)     

Stability of Macroscopic Binary Systems

The Darwin instability effect in the binary systems(di-planets, di-stars, and di-galaxies) is analyzed within the model based on the Regge-like laws. All possible binary stars are found satisfying the Darwin instability condition that requires to search for other mechanism triggering the merger of the contact binary objects. New analytical formulas are obtained for the orbital rotation period and the relative distance between components of the binary system. The decreasing and increasing periods as functions of mass asymmetry are related, respectively, with the non-overlapping and overlapping stage of the binary object evolution.     

Macroscopic Dimension of 3-Manifolds

In this paper we give the answer to the Gromov's question about the macroscopic dimension of universal coverings of closed manifolds in dimension 3. We prove that the macroscopic dimension of a universal covering of a closed Riemannian 3-manifold cannot be equal to 2.     

Macroscopic realizations of quantum logics

Summary Two-particle quantum systems with spin can be simulated by classical automata described by graphs. These graphs are associated with nondistributive property lattices of these quantum systems. We emphasize that to non-local properties of a quantum system being in a certain eigenstate of the permutation operator there correspond merely some additional vertices in the graph which have nothing nonlocal in their nature. This leads to the possibility of violating Bell's inequalities in classical systems described by graphs (see Section 6) without violating relativity theory.The subjective interpretation of quantum mechanics of von Neumann, London, and Bauer can be connected with the Boolean nature of mind grasping the non-Boolean nature of the world, which results in the projection postulate: wave packet reduction. A simple example is given for a two-particle system with spin.     

Macroscopic Approach to Quantum Optics

This paper investigates how an approach alternative to the canonical quantization schemes may be used to describe Quantum Optics phenomena. By utilizing the approach pioneered by Keldysh, we derive equations for the time dependent correlation functions of the quantized optical fields. These contain the coupling to matter in linear and nonlinar response functions which replace the material parameters of phenomenological macroscopic theories. We present these results as alternatives to existing theoretical methods in Quantum Optics. The paper presents the general formulation of the theory, derives the equations in some specific cases relating to non‐linear optics, and solves some illustrative special cases. We regain known results but also some additional terms deriving from the quantum fluctuations of the material media.     

Macroscopic quantum coherence in ferritin

In a breakthrough experiment, Awschalom et al. [Phys. Rev. Lett. 68, 3092 (1992)] have demonstrated that the antiferromagnetic core in ferritin resonates between two states with oppositely directed Néel vectors, making it the first observation of MQC. A theory has been developed for this resonance including the effect of the 100 or so⁵⁷Fe nuclear spins expected in each ferritin core. Since the hyperfine coupling is known to be ～68 MHz and the MQC frequency is ～1 MHz, the degeneracy of the Néel states, and with it, the MQC resonance, is destroyed in all ferritin particles except those with zero total staggered nuclear spin. From the measured size of λ″(ω), the energy being absorbed by the ferritin is at least 4000 times larger than the maximum permissible. Hence, the true importance of these experiments lies not in the narrow issue of MQC, but in the disproof of long cherished theoretical conservation laws.     

Macroscopic resonances in planar geometry

Resonating response is a characteristic feature of free-particle system contained between two vibrating planar surfaces. Resonance frequencies and widths are determined by a mean period of motion of particles reflected from the walls. Resonances due to quasiperiodic macroscopic motion appear when the interaction among quasi-particles by means of perturbations of the common self-consistent field is included. They have finite widths corresponding to collisionless Landau dissipation. Possible relationship of this phenomenon to nuclear giant resonances is discussed.     

Macroscopic short-time electrodynamics for conductors

In the macroscopic electrodynamics (MED) of good conductors (metals) based on Ohm's law j=E, the momentum relaxation time =m/ne² of the electrons limits the application to electromagnetic (EM) processes with characteristic timest. An interesting physical difficulty occurs in MED since the EM field damping time _R=/ of metals is very small compared with the minimum macroscopic time scale, _R. Consequently, the damping and propagation of EM waves and pulses in good conductors cannot be correctly described within the frame of conventional MED. New hyperbolic EM wave equations with relaxation and memory are proposed, which no longer exhibit the _R deficiency. The latter is caused by Ohm's law, which breaks down for short-time processes, due to neglect of electron inertia. The advantages of the proposed and the disadvantages of the conventional EM wave equations for good conductors are discussed in applications.