Metastable states,the adiabatic theorem and parity violating geometric phases I

A system of metastable plus unstable states is discussed. The mass matrix governing the time development of the system is supposed to vary slowly with time. The adiabatic limit for this case is studied and it is shown that only the metastable states obtain the analogs of the dynamical and geometrical phase factors familiar from stable states. Abelian and non-Abelian geometric phase factors for metastable states are defined.     

Metastable states,the adiabatic theorem and parity violating geometric phases II

We discuss and calculate parity conserving (PC) and parity violating (PV) geometric phases for the metastable 2S states of hydrogen and deuterium. The atoms are supposed to be subjected to slowly varying electric and magnetic fields which act as external parameters for the atoms. Geometric flux density fields are introduced which allow for an easy overview how to choose the paths in parameter space in order to obtain only PC or only PV geometric phases. The PV phases are calculated in the Standard Model of particle physics. Even if numerically they come out small they have interest of principle as a new manifestation of parity violation in atomic physics. Electronic supplementary material Supplementary Online Material     

Metastable states and coexistence of phases in scaling theory

The methods of scaling theory are used to investigate the physical properties of matter in a large neighborhood of the stability boundary (spinodal), including metastable states and lines of phase equilibrium. Expressions are obtained for the pressure isotherms in metastable gas and liquid phases, a phase equilibrium equation, and an expression for the width of the metastable region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 73–77, March, 1981.We thank V. M. Sysoev and Yu. I. Shimanskii for valuable comments and for discussing the results.     

Observation of geometric phases for mixed states using NMR interferometry

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well-understood, noiseless, pure-state case.     

Metastable phases in Gallium-Indium eutectic alloy particles and their size dependence

In this paper, submicrometer-sized Ga-In eutectic alloy particles were dispersed into polymethylmethacrylate (PMMA) matrix by ultrasonic vibration and sedimentation method. The solidification and melting processes of Ga-In eutectic alloy particles were studied by differential scanning calorimeter (DSC). Four endothermal peaks with the onset temperature located at 16, −11, −22, and −27 °C were observed in DSC heating curves, which corresponded to the melting process of the stable Ga-In phase α-Ga(In) and three metastable phases of β-Ga(In), δ-Ga(In) and γ-Ga(In), respectively. The stable phase α-Ga(In) can only be formed when the size of alloy particle was larger than 0.58 μm. Conversely, metastable phases β-Ga(In), δ-Ga(In) and γ-Ga(In) are mainly formed. The result shows that phase structures in Ga-In eutectic alloy are size dependent.     

Metastable states of molecules

We define metastable states to be density matrices which are at local minima of a certain non-linear functional, and investigate their general properties, proving in particular that the metastable states are not necessarily unique but are modified Gibbs states. The case of an atom in an external electric field is investigated in some detail.     

Metastable states in Si:H

The results of ab initio LDF calculations applied to large clusters of Si atoms containing H in various positions are described. We find the bond centred (BC) defect to be most stable for neutral and positively charged H. H placed at an antibonding site is also stable with an energy 0.1 eV higher than the BC defect. The stability of H₂ and H^*₂ is also discussed. New results are reported for the conversion of BC defects into Si dangling bonds. It is found that H attached to vacancy-like defects is bi-stable: for Si-H-Si lengths less than ≈3.8 Å, the BC defect is stable, whereas for longer separations, the Si-H ··· Si dangling bond is stable. A discussion of the relevance of this to the Staebler-Wronski effect is given.     

Metastable states of dust plasma

The free energy of three-component dust plasma has been calculated analytically based on the spherical model of an elementary electroneutral volume. It has been shown that metastable states of dust particles, ions, and simultaneously all plasma particles can exist for finite interparticle distances. These states can be attained due to spatial correlation of electrons, while some states can be attained due to the correlation of ions. A large charge of dust particles, high electron temperature, and a small fraction of the charge of the electrons compared to the total absolute charge of the plasma particles are important conditions for the existence of metastable states. A possible connection between the existence of metastable states of particles in the plasma and their agglomeration has been analyzed.     

Quantization,coherent states and geometric phases of a generalized nonstationary mesoscopic RLC circuit

We present an alternative quantum treatment for a generalized mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Taking advantage of the Lewis and Riesenfeld quantum invariant method and using quadratic invariants we obtain exact nonstationary Schrödinger states for this electromagnetic oscillation system. Afterwards, we construct coherent and squeezed states for the quantized RLC circuit and employ them to investigate some of the system’s quantum properties, such as quantum fluctuations of the charge and the magnetic flux and the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary mesoscopic circuit. Finally we evaluate the dynamical and Berry phases for three special circuits. Surprisingly, we find identical expressions for the dynamical phase and the same formulae for the Berry’s phase.     

Nodal free geometric phases: Concept and application to geometric quantum computation

Nodal free geometric phases are the eigenvalues of the final member of a parallel transporting family of unitary operators. These phases are gauge invariant, always well defined, and can be measured interferometrically. Nodal free geometric phases can be used to construct various types of quantum phase gates.     

Metastable superpositions of ortho- and para-Helium states

We analyze superpositions of ortho- and para-Helium states, considering the possible existence of stationary and metastable states in the system. In particular, the metastable superposition of 1s2s ortho- and para-states seems to be accessible to experimental scrutiny.     

Metastable states of quantum lattice systems

We extend the characterisation of metastability, as given in [1] for classical systems, to show that quantal lattice systems with suitable long range forces can support metastable states.     

Metastable states of antiprotonic helium atoms

We discuss the latest theoretical achievements in calculations of energy transitions in the antiprotonic helium He⁺ p-0304; atoms. New variational calculations of the nonrelativistic energies with precision of ∼10^-10 a.u. and relativistic and QED corrections to the energy levels of mα ⁵ order are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Base-controlled mechanical systems and geometric phases

In this paper, we carry a detailed study of mechanical systems with configuration space Q?Q/G$Q?Q/G$ for which the base Q/G$Q/G$ variables are being controlled. The overall system’s motion is considered to be induced from the base one due to the presence of general non-holonomic constraints. It is shown that the solution can be factorized into dynamical and geometrical parts. Moreover, under favorable kinematical circumstances, the dynamical part admits a further factorization since it can be reconstructed from an intermediate (body) momentum solution, yielding a reconstruction phase formula. Finally, we apply this results to the study of concrete mechanical systems.     

Coherent states and geometric quantization

Based on the concept of generalized coherent states, a theory of mechanical systems is formulated in a way which naturally exhibits the mutual relation of classical and quantum aspects of physical phenomena.This work was supported in part by The Swedish Institute