Quantum Rotators Research Articles

Quantum Impurity Rotator in a Matrix of Quantum Rotors: Electron Paramagnetic Resonance Dynamics of CH3 in Solid CD4 Matrix

The rotational dynamics and the geometry of a light and flexible impurity molecule like methyl, matrix isolated in van der Waals solid, are supposed to be sensitive to the host molecule dynamics and order alterations of the matrix. In addition, the location of the impurity and its interaction with the matrix molecules is of prime importance. Large energy gaps between rotation levels of quantum rotators allow precise investigation of temperature-assisted quantum tunneling effects. The molecular rotation of methyl radicals isolated in the deuterated solid methane isotopomer, CD4, was investigated both by experimental and theoretical electron paramagnetic resonance (EPR) methods. The reduction of the quantum rotation frequency evident from the EPR spectrum of methyl radical at liquid-He temperatures was explained and connected to the irregular ratio of the central doublet to the outer quartet hf transitions. The involvement of temperature in the alteration of methyl symmetry between the C3 and D3 groups and the molecular host-host and guest-host interaction strengths were also examined by constructing temperature profiles of the rotation correlation times in the three phases of solid methane. The present study proves the deep impact that a van der Waals matrix may have on the geometry and the rotation levels of a substitutionally trapped quantum impurity rotor, effects that are yet very little known. This close correlation between dynamics of an impurity particle and the matrix molecules has great potential in developing sensitive physicochemical probes for van der Waals solids.

Kinetic approach to condensation: Diatomic gases with dipolar molecules.

We derive a kinetic equation for rarefied diatomic gases whose molecules have a permanent dipole moment. Estimating typical parameters of such gases, we show that quantum effects cannot be neglected when describing the rotation of molecules, which we thus approximate by quantum rotators. The intermolecular potential is assumed to involve an unspecified short-range repulsive component and a long-range dipole-dipole Coulomb interaction. In the kinetic equation derived, the former and the latter give rise, respectively, to the collision integral and a self-consistent electric field generated collectively by the dipoles (as in the Vlasov model of plasma). It turns out that the characteristic period of the molecules' rotation is much shorter than the time scale of the collective electric force and the latter is much shorter than the time scale of the collision integral, which allows us to average the kinetic equation over rotation. In the averaged model, collisions and interaction with the collective field affect only those rotational levels of the molecules that satisfy certain conditions of synchronism. It is then shown that the derived model does not describe condensation; i.e., permanent dipoles of molecules cannot exert the level of intermolecular attraction necessary for condensation. It is argued that an adequate model of condensation must include the temporary dipoles that molecules induce on each other during interaction, and that this model must be quantum, not classical.

A quantum Mermin–Wagner theorem for quantum rotators on two-dimensional graphs

This is the first of a series of papers considering symmetry properties of quantum systems over 2D graphs or manifolds, with continuous spins, in the spirit of the Mermin–Wagner theorem [N. D. Mermin and H. Wagner, “Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models,” Phys. Rev. Lett. 17, 1133–1136 (1966)]10.1103/PhysRevLett.17.1133. In the model considered here (quantum rotators), the phase space of a single spin is a d-dimensional torus M, and spins (or particles) are attached to sites of a graph \documentclass[12pt]{minimal}\begin{document}$(\Gamma ,\mathcal {E})$\end{document}(Γ,E) satisfying a special bi-dimensionality property. The kinetic energy part of the Hamiltonian is minus a half of the Laplace operator −Δ/2 on M. We assume that the interaction potential is C2-smooth and invariant under the action of a connected Lie group \documentclass[12pt]{minimal}\begin{document}${\tt G}$\end{document}G (i.e., a Euclidean space \documentclass[12pt]{minimal}\begin{document}${\mathbb {R}}^{d^{\prime }}$\end{document}Rd′ or a torus M′ of dimension d′ ⩽ d) on M preserving the flat Riemannian metric. A part of our approach is to give a definition (and a construction) of a class of infinite-volume Gibbs states for the systems under consideration (the class \documentclass[12pt]{minimal}\begin{document}$\mathfrak {G}$\end{document}G). This class contains the so-called limit Gibbs states, with or without boundary conditions. We use ideas and techniques originated from papers [R. L. Dobrushin and S. B. Shlosman, “Absence of breakdown of continuous symmetry in two-dimensional models of statistical physics,” Commun. Math. Phys. 42, 31–40 (1975)10.1007/BF01609432; C.-E. Pfister, “On the symmetry of the Gibbs states in two-dimensional lattice systems,” Commun. Math. Phys. 79, 181–188 (1981)10.1007/BF01942060; J. Fröhlich and C. Pfister, “On the absence of spontaneous symmetry breaking and of crystalline ordering in two-dimensional systems,” Commun. Math. Phys. 81, 277–298 (1981)10.1007/BF01208901; B. Simon and A. Sokal, “Rigorous entropy-energy arguments,” J. Stat. Phys. 25, 679–694 (1981)10.1007/BF01022362; D. Ioffe, S. Shlosman and Y. Velenik, “2D models of statistical physics with continuous symmetry: The case of singular interactions,” Commun. Math. Phys. 226, 433–454 (2002)]10.1007/s002200200627 in combination with the Feynman–Kac representation, to prove that any state lying in the class \documentclass[12pt]{minimal}\begin{document}$\mathfrak {G}$\end{document}G (defined in the text) is \documentclass[12pt]{minimal}\begin{document}${\tt G}$\end{document}G-invariant. An example is given where the interaction potential is singular and there exists a Gibbs state which is not \documentclass[12pt]{minimal}\begin{document}${\tt G}$\end{document}G-invariant. In the next paper, under the same title we establish a similar result for a bosonic model where particles can jump from a vertex i ∈ Γ to one of its neighbors (a generalized Hubbard model).

Planets as quantum rotators of the boson and fermion types—relics of elite plasma rings

Planets as quantum rotators of the boson and fermion types—relics of elite plasma rings

Translation and reorientation of CD4 molecules in nanoscale cages of zeolites as studied by deuteron spin-lattice relaxation

Deuteron spin-lattice relaxation was applied to study translational and rotational mobility of CD(4) molecules trapped in the cages of zeolites. Tetrahedral methane molecules are treated as quantum rotators. Relaxation rates related to the intraquadrupole interaction are derived for the T and A+E symmetry species in the presence of large tunneling splittings, consistently with the assumption that A and E species molecules relax at the same rate. An exchange model is presented, which describes the effect on relaxation of CD(4) jumping between two positions characterized by different potentials. While staying at either position bonded to an atom or ion at the cage wall, the molecule has some freedom to move in the vicinity. This causes a time-dependent external electric field gradient, which contributes to the deuteron relaxation rate via the electric quadrupole interaction. Spin conversion transitions couple the relaxation of magnetizations M(T) and M(AE), which is taken into account by reapplying the presented model under somewhat different conditions. Such a two-step procedure leads to successful fits with the experimental results obtained in the range of temperatures roughly 20-200 K for zeolites HY, NaA, and NaMordenite. At higher temperatures CD(4) molecules fly freely across zeolite cages and relaxation changes accordingly, while incoherent tunneling dominates for immobile molecules below 20 K.

Dual oscillators and quantum pendulums: Spectrum and correlators

We outline the nonlinear transformation in the path integral representation for partition function of $O(N)$ symmetric oscillator systems bringing their duality to certain one-dimensional oscillators with unstable potential shapes. This duality transformation realizes the equivalence between spectra of a Hermitian and a non-Hermitian Hamiltonian. It is exploited to calculate exactly the spectra of quantum rotators. The zero-temperature limit is considered and the dual representation of $n$-point correlators of coordinate operators is obtained.

NH 3 quantum rotators in Hofmann clathrates: intensity and width of rotational transition lines

Inelastic structure factors for rotational transitions of uniaxial NH 3 quantum rotators, measured in a Hofmann clathrate with biphenyl as guest molecule, agree with those calculated for free rotators. A finite intrinsic line width, found for rotational transitions involving the rotational level j=3 at low temperature, supports a recently suggested model based on resonant rotor–rotor coupling.

Hidden-crossing transitions between collective states of coupled quantum rotators as a possible mechanism of memory processing

The possibility that memory is related to the collective rotational energy levels of the molecules is considered. Treating the molecule as a quantum rotator, the probability of the “hidden-crossing” transitions between rotational states, induced by the external periodic electric field, is analyzed. It is found that this probability depends on frequency only, i.e. the external signal causes the information transfer rather than the energy. Using the data of the typical sources of electric signals in brain cells and the criterium of maximization of the information entropy, the relevant number of water molecules (rotators) per cell is estimated. The results appear to be close to the actual number of water molecules per cortical neuron.

Diffusion monte carlo methods with a fixed number of walkers

In this paper we discuss various aspects of diffusion Monte Carlo methods using a fixed number of walkers. First, a rigorous proof of the divergence of pure diffusion Monte Carlo (PDMC) methods (DMC without branching in which the weights are carried along trajectories) is given. Second, a bias-free Monte Carlo method combining DMC and PDMC approaches, and based on a minimal stochastic reconfiguration of the population, is discussed. Finally, some illustrative calculations for a system of coupled quantum rotators are presented.

The one-particle energy spectrum of weakly coupled quantum rotators

The ground state of a lattice model of weakly interacting quantum rigid rotators is analyzed by the cluster expansion method applied to its Feynman–Kac representation. The Hamiltonian of the infinite crystal in the ground state is shown to have a branch of absolutely continuous spectrum separated by gaps from the rest of the spectrum, describing the one-particle excitations.

Bounds on Correlation Functions of Quantum Rotators

We derive a McBryan–Spencer bound to the correlation function of a one-dimensional array of quantum rotators in the Villain approximation of the cosine interaction. We obtain the partition function of the system in the gas representation and establish a lower bound on the external charges correlation function. We also discuss the possible existence of a Kosterlitz–Thouless phase for the quantum rotators in the Villain approximation.

Partial conversion of neutron incoherent into coherent scattering by NH 3 quantum rotators

Neutron diffraction experiments on powders are used to investigate the quantum mechanical behaviour of uniaxial rotators, i.e. NH 3-molecules in Ni(NH 3) 6(PF 6) 2, Co(NH 3) 6(PF 6) 2 and Ni(NH 3) 6I 2. A diffuse temperature dependent component of the total scattering, modulated ∼ sin Qr H-H/ Qr H-H, is observed at a temperature of ≃ 20 K and below. This observation is due to the fact, that on cooling the sample to kT ∼ B (rotational constant) the rotational ground state is strongly populated. The ground state of a uniaxial free rotator, however, is completely polarized. As a consequence the scattering of those NH 3 groups being in the ground state becomes coherent and is observable in diffraction experiments.

Localization in the ground state of a disordered array of quantum rotators

We consider the zero-temperature behavior of a disordered array of quantum rotators given by the finite-volume Hamiltonian: $$H_\Lambda = - \mathop \Sigma \limits_{x \in \Lambda } \frac{{h(x)}}{2}\frac{{\partial ^2 }}{{\partial \varphi (x)^2 }} - J\mathop \Sigma \limits_{\left\langle {x,y} \right\rangle \in \Lambda } \cos (\varphi (x) - \varphi (y))$$ , wherex,y∈Z d , 〈,〉 denotes nearest neighbors inZ d ;J>0 andh={h(x)>0,x∈Z d } are independent identically distributed random variables with common distributiondμ(h), satisfying ∫h −δ dμ(h) 0. We prove that for anym>0 it is possible to chooseJ(m) sufficiently small such that, if 0<J<J(m), for almost every choice ofh and everyx∈Z d the ground state correlation function satisfies $$\left\langle {\cos (\varphi (x) - \varphi (y))} \right\rangle \leqq C_{x,h,J} e^{ - m\left| {x - y} \right|} $$ for ally∈Z d withC x,h,J <∞.

Path-integral Monte Carlo techniques for rotational motion in two dimensions: Quenched, annealed, and no-spin quantum-statistical averages.

We provide a path-integral Monte Carlo (PIMC) technique for two-dimensional quantum rotators in static potentials. In our PIMC scheme we perform the summations over the different homotopy classes on the circle. In the case of a homonuclear diatomic molecule the coupling of nuclear spin and rotations due to the symmetry requirement of the total wave function is also taken into account in the PIMC technique. We introduce different experimentally relevant PIMC averaging procedures, revealing the quantum effects due to discrete level spacing and exchange, and compare with analytical results.

Orientational ordering in solid hydrogen

The orientational ordering in solid ortho–para hydrogen mixtures is reviewed with emphasis on dilute mixtures for which a glass-like freezing of the randomly distributed quantum rotators is observed. The interpretation of the various nuclear magnetic resonance experiments used to monitor the relevant order parameters is discussed, and a summary is given of the current consensus and outstanding problems concerning the nature of the ordering in random dilute mixtures.

The structure of hydrogen chloride gas

A new experiment to measure the intermolecular partial structure factors for hydrogen chloride gas (e.g. H-H structure factor, etc.) at a temperature of 355·7 K and density 0·29 × 1028 molecules m-3, by neutron diffraction and isotopic substitution, is described. Data with good counting statistics and corrected for many side effects are required. Observed scattering patterns are complicated by the large, incoherent, energy and angle-dependent, single molecule scattering function. This function is shown to be independent of density to about 5 per cent for the gas densities, and can be simulated to good accuracy by a calculation based on an ideal gas of quantum rotators. Partial structure factors obtained in this experiment provide a standard on which to test models of the intermolecular potential.