Quantum Mechanics is About Quantum Information

I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive---just as, following Einsteins special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical entity in its own right.     

The Reality in Bohmian Quantum Mechanics or Can You Kill with an Empty Wave Bullet?

Several situations, in which an empty wave causes an observable effect, are reviewed. They include an experiment showing surrealistic trajectories proposed by Englert et al. and protective measurement of the density of the quantum state. Conditions for observable effects due to empty waves are derived. The possibility (in spite of the existence of these examples) of minimalistic interpretation of Bohmian quantum mechanics in which only Bohmian positions supervene on our experience is discussed.     

Weak Measurements from the Point of View of Bohmian Mechanics

The theory of weak measurements developed by Aharonov and coworkers has been applied by them and others to several interesting problems in which the system of interest is both pre- and post-selected. When the probability of successful post-selection is very small the prediction for the weak value of the measured quantity is often bizarre and sometimes controversial, lying outside the range of possibility for a classical system or for a quantum system in the absence of post-selection (e.g. negative kinetic energies associated with particles found immediately after the weak measurement deep inside a classically forbidden region). In Bohmian mechanics a quantum particle is postulated to be a point-like particle which is always accompanied by a wave which probes its environment and guides its motion accordingly. Hence, from the point of view of this theory, it is natural to ask whether the measured weak value under consideration is a property of the point-like particle or of the wave (or of both) and what, if anything, it is that is actually being measured. In this paper, weak measurements of position, momentum and kinetic energy are considered for very simple case studies with these questions in mind.     

Conformational analysis of methylphenidate: comparison of molecular orbital and molecular mechanics methods

Summary Methylphenidate (MP) binds to the cocaine binding site on the dopamine transporter and inhibits reuptake of dopamine, but does not appear to have the same abuse potential as cocaine. This study, part of a comprehensive effort to identify a drug treatment for cocaine abuse, investigates the effect of choice of calculation technique and of solvent model on the conformational potential energy surface (PES) of MP and a rigid methylphenidate (RMP) analogue which exhibits the same dopamine transporter binding affinity as MP. Conformational analysis was carried out by the AM1 and AM1/SM5.4 semiempirical molecular orbital methods, a molecular mechanics method (Tripos force field with the dielectric set equal to that of vacuum or water) and the HF/6-31G* molecular orbital method in vacuum phase. Although all three methods differ somewhat in the local details of the PES, the general trends are the same for neutral and protonated MP. In vacuum phase, protonation has a distinctive effect in decreasing the regions of space available to the local conformational minima. Solvent has little effect on the PES of the neutral molecule and tends to stabilize the protonated species. The random search (RS) conformational analysis technique using the Tripos force field was found to be capable of locating the minima found by the molecular orbital methods using systematic grid search. This suggests that the RS/Tripos force field/vacuum phase protocol is a reasonable choice for locating the local minima of MP. However, the Tripos force field gave significantly larger phenyl ring rotational barriers than the molecular orbital methods for MP and RMP. For both the neutral and protonated cases, all three methods found the phenyl ring rotational barriers for the RMP conformers/invertamers (denoted as cte, tte, and cta) to be: cte, tte> MP > cta. Solvation has negligible effect on the phenyl ring rotational barrier of RMP. The B3LYP/6-31G* density functional method was used to calculate the phenyl ring rotational barrier for neutral MP and gave results very similar to those of the HF/6-31G* method.     

Elastic properties of poly(hydroxybutyrate) molecules

Elasticity of various poly(hydroxybutyrate) (PHB) molecules of regular and irregular conformational structure was examined by the molecular mechanics (MM) calculations. Force - distance functions and the Young's moduli E were computed by stretching of PHB molecules. Unwinding of the 2(1) helical conformation H is characterized at small deformations by the Young's modulus E = 1.8 GPa. The H form is transformed on stretching into the highly extended twisted form E, similar to the beta-structure observed earlier by X-ray fiber diffraction. The computations revealed that in contrast to paraffins, the planar all-trans structure of undeformed PHB is bent. Hence, a PHB molecule attains the maximum contour length in highly straightened, but slightly twisted conformations. A dependence of the single-chain moduli of regular and disordered conformations on the chain extension ratio x was found. The computed data were used to analyze elastic response of tie (bridging) molecules in the interlamellar (IL) region of a semi-crystalline PHB. A modification of the chain length distribution function of tie molecules tau(N) due to secondary crystallization of PHB was conjectured. The resulting narrow distribution tau(N) comprises the taut tie molecules of higher chain moduli prone to overstressing. The molecular model outlined is in line with the macroscopically observed increase in the modulus and brittleness of PHB with storage time.     

Bell's Inequality for Two-Particle Mixed Spin States

We derive the Bell–Clauser–Horne–Shimony–Holt inequalities for two-particle mixed spin states both in the conventional quantum mechanics and in the hidden-variables theory. We consider two cases for the vectors , and specifying the axes onto which the particle spins of a correlated pair are projected. In the first case, all four vectors lie in the same plane, and in the second case, they are oriented arbitrarily. We compare the obtained inequalities and show that the difference between the predictions of the two theories is less for mixed states than for pure states. We find that the inequalities obtained in quantum mechanics and the hidden-variables theory coincide for some special states, in particular, for the mixed states formed by pure factorable states. We discuss the points of similarity and difference between the uncertainty relations and Bell's inequalities. We list all the states for which the right-hand side of the Bell–Clauser–Horne–Shimony–Holt inequality is identically equal to zero.     

The Riemann Surface of the Chiral Potts Model Free Energy Function

In a recent paper we derived the free energy or partition function of the N-state chiral Potts model by using the infinite lattice inversion relation method, together with a non-obvious extra symmetry. This gave us three recursion relations for the partition function per site T _pq of the infinite lattice. Here we use these recursion relations to obtain the full Riemann surface of T _pq . In terms of the t _p ,t _q variables, it consists of an infinite number of Riemann sheets, each sheet corresponding to a point on a (2N–1)-dimensional lattice (for N>2). The function T _pq is meromorphic on this surface: we obtain the orders of all the zeros and poles. For N odd, we show that these orders are determined by the usual inversion and rotation relations (without the extra symmetry), together with a simple linearity ansatz. For N even, this method does not give the orders uniquely, but leaves only [(N+4)/4] parameters to be determined.     

Hermiticity of Quantum Observables Versus Commutation Relations

In order to obtain sum rules and spectral representations the Hermiticity property , A = A, of observables is used. It is shown that for certain and the property turns out to be inconsistent with the commutation relations that contain A. The known Schwinger paradox is explained by this inconsistency.     

Quantum Trajectories, State Diffusion, and Time-Asymmetric Eventum Mechanics

We show that the quantum stochastic Langevin model for continuous in time measurements provides an exact formulation of the von Neumann uncertainty error-disturbance principle. Moreover, as it was shown in the 1980s, this Markov model induces all stochastic linear and nonlinear equations of the phenomenological informational dynamics such as quantum state diffusion and spontaneous localization by a simple quantum filtering method. Here we prove that the quantum Langevin equation is equivalent to a Dirac-type boundary-value problem for the second quantized input offer waves from future in one extra dimension, and to a reduction of the algebra of the consistent histories of past events to an Abelian subalgebra for the trajectories of the output particles. This result supports the wave-particle duality in the form of the thesis of Eventum Mechanics that everything in the future is constituted by quantized waves, everything in the past by trajectories of the recorded particles. We demonstrate how this time arrow can be derived from the principle of quantum causality for nondemolition continuous in time measurements.