Why Bohm's Quantum Theory?

This is a brief reply to S. Goldstein's article Quantum theory without observers in Physics Today. It is pointed out that Bohm's pilot wave theory is successful only because it keeps Schrödinger's (exact) wave mechanics unchanged, while the rest of it is observationally meaningless and solely based on classical prejudice.     

A Continuous Transition Between Quantum and Classical Mechanics. I

In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of mechanics which provides a continuous transition between quantum and classical mechanics via environment-induced decoherence.     

Copenhagen quantum mechanics

In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists’ laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr’s quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.     

Controlling quantum discord dynamics in cavity QED systems by applying a classical driving field with phase decoherence

We investigate a two-level atom interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence and find that a stationary quantum discord can arise in the interaction of the atom and cavity field as the time turns to infinity.We also find that the stationary quantum discord can be increased by applying a classical driving field.Furthermore,we explore the quantum discord dynamics of two identical non-interacting two-level atoms independently interacting with a quantized cavity field and a classical driving field in the presence of phase decoherence.Results show that the quantum discord between two atoms is more robust than entanglement under phase decoherence and the classical driving field can help to improve the amount of quantum discord of the two atoms.     

量子力学矩阵元的经典极限

本研究了量子力学矩阵元的经典极限，用新的方法证明了如下定理；在分立谱情况下，量子力学矩阵元ｆｎｍ的经典极限是相应经典力学量ｆ（ｔ）之Ｆｏｕｒｉｅｒ级数展开的第ｎ－ｍ个分量；在连续谱情况下，量子力学矩阵元ｆＥＥ与Ｐｌａｃｋ常量ｈ的乘积ｈｆＥＥ的经典极限相应经典力学量ｆ（ｔ）之Ｆｏｒｉｅｒ积分展开的第ω次分量。     

Inconsistency of Quantum—Classical Dynamics, and What it Implies

A new proof of the impossibility of a universal quantum-classical dynamics is given. It has at least two consequences. The standard paradigm “quantum system is measured by a classical apparatus” is untenable, while a quantum matter can be consistently coupled only with a quantum gravity.     

量子谐振子与经典谐振子的比较

运用广义线性量子变换的普遍理论求解了量子谐振子,同经典谐振子比较给出了量子谐振子趋近于经典极限的条件,并得出相干态是最理想的经典极限态．     

Classical limit of scattering in quantum mechanics—A general approach

The classical and quantum physics seem to divide nature into two domains macroscopic and microscopic. It is also certain that they accurately predict experimental results in their respective regions. However, the reduction theory, namely, the general derivation of classical results from the quantum mechanics is still a far cry. The outcome of some recent investigations suggests that there possibly does not exist any universal method for obtaining classical results from quantum mechanics. In the present work we intend to investigate the problem phenomenonwise and address specifically the phenomenon of scattering. We suggest a general approach to obtain the classical limit formula from the phase shiftδ _l, in the limiting value of a suitable parameter on whichδ _l depends. The classical result has been derived for three different potential fields in which the phase shifts are exactly known. Unlike the current wisdom that the classical limit can be reached only in the high energy regime it is found that the classical limit parameter in addition to other factors depends on the details of the potential fields. In the last section we have discussed the implications of the results obtained.     

等权波包与一维简谐振子

以第n个定态波函数为中心,将其附近的从第（n-N）个到（n N）个共2N 1个定态波函数以等权重1/√2N 1叠加起来,就构成了所谓的等权波包,波包上任一力学量f的平均值f^-在经典极限下有严格的经典对应,这一结果可用来考察以往用波包讨论量子力学经典极限的得失之处,本较系统地研究了一维简谐振子体系,给出了若干新结果,并澄清了现行教科书中若干不甚正确的说法。     

Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.     

Dynamical Suppression of Pure Amplitude Damping in Two-State Quantum Systems

Dynamical control of decoherence induced by the environment in a single quantum-bit system is investigated. We choose the suitable perturbations acting on the qubit system to decrease the decoherence due to pure amplitude damping. The scheme proposed here is based on the free-Hamiltonian-elimination technique and the paritykick technique, which concludes two homogeneous classical large-blue-detuned optical fields with different frequencies added to the qubit system. By applying this scheme, the decoherence can be completely suppressed.     

Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.     

The quantum measurement problem and selection of classical states

The problem of selection of preferred basis during passage from quantum to classical systems is treated with the help of a simple example of a 2-state system like the sugar molecule. A simple principle leading to this selection is stated and demonstrated in case of the chosen example. The principle, stated simply is that the preferred basis is the one in which the system environment interaction hamiltonian is diagonal. Talk given at the International Symposium on Theoretical Physics, Bangalore, November 1984.     

Dynamical Suppression of Pure Amplitude Damping in Two-State Quantum Systems

Dynamical control of decoherence induced by the environment in a single quantum-bit system is investigated. We choose the suitable perturbations acting on the qubit system to decrease the decoherence due to pure amplitude damping. The scheme proposed here is based on the free-Hamiltonian-elimination technique and the paritykick technique, which concludes two homogeneous classical large-blue-detuned optical fields with different frequencies added to the qubit system. By applying this scheme, the decoherence can be completely suppressed.     

Principles of maximally classical and maximally realistic quantum mechanics

Recently Auberson, Mahoux, Roy and Singh have proved a long standing conjecture of Roy and Singh: In 2N-dimensional phase space, a maximally realistic quantum mechanics can have quantum probabilities of no more than N+1 complete commuting cets (CCS) of observables coexisting as marginals of one positive phase space density. Here I formulate a stationary principle which gives a nonperturbative definition of a maximally classical as well as maximally realistic phase space density. I show that the maximally classical trajectories are in fact exactly classical in the simple examples of coherent states and bound states of an oscillator and Gaussian free particle states. In contrast, it is known that the de Broglie-Bohm realistic theory gives highly nonclassical trajectories.