Phase transitions and heterophase fluctuations

Abstract This review is devoted to a detailed description of quasiequilibrium systems in which phase transitions are accompanied by heterophase fluctuations. The latter lead to the appearance of the so-called pretransitional, or precursor, phenomena. A comprehensive analysis of the nature of these fluctuations is given. A great number of experiments displaying the presence of heterophase fluctuations is discussed. The main features of phenomenological models for heterophase systems are elucidated. A microscopic statistical theory of systems with heterophase fluctuations is presented. The theory is illustrated by the crystal-liquid and ferromagnet-paramagnet phase transitions. The theory makes it possible to explain. from a single general point of view, many experimental anomalies observed around phase-transition points in different systems.

[1]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[2]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[3]  A. L. Kuzemsky,et al.  Nonequilibrium Statistical Thermodynamics , 2017 .

[4]  V. Yukalov Spaces of states for heterophase systems , 1982 .

[5]  J. Wilks,et al.  The Properties of Liquid and Solid Helium , 1968 .

[6]  William Alan Day,et al.  The Thermodynamics of Simple Materials with Fading Memory , 1972 .

[7]  S. Horuzhy Introduction to Algebraic Quantum Field Theory , 1990 .

[8]  Yukalov Theory of melting and crystallization. , 1985, Physical review. B, Condensed matter.

[9]  H. Hirsch Note on the Paper “Gibbs vs. Shannon Entropies” by Richard L. Liboff , 1975 .

[10]  John Ziman,et al.  Models of disorder , 1979 .

[11]  A. Gavrielides,et al.  Molecular Motion in the Ferroelectric Phase of Hydrogen Chloride , 1971 .

[12]  J. Barker,et al.  What is "liquid"? Understanding the states of matter , 1976 .

[13]  M. A. Krivoglaz Fluctuon states of electrons , 1974 .

[14]  P. Knight,et al.  Ions that fit into place , 1988, Nature.

[15]  M. Tinkham,et al.  Fluctuations near superconducting phase transitions , 1975 .

[16]  J. Brookeman,et al.  Cl 35 nuclear quadrupole resonance study of the ferroelectric transition in HCl and in the mixed crystals HCl-DCl , 1980 .

[17]  A. Shumovsky,et al.  Metastable heterophase system of the Ising type , 1985 .

[18]  G. Aeppli,et al.  Metamagnets and frustration , 1984 .

[19]  I. Ventura Macroscopic solitons in thermodynamics , 1981 .

[20]  H. Cook Droplet model for central phonon peaks , 1977 .

[21]  Alain Guichardet,et al.  Symmetric Hilbert spaces and related topics , 1972 .

[22]  G. V. Chester The theory of irreversible processes , 1963 .

[23]  G. D'arrigo Sound propagation in moderately supercooled liquids. A comparison with water , 1981 .

[24]  V. Yukalov A new method in the theory of phase transitions , 1981 .

[25]  A. G. Klimenko,et al.  The Effect of Amorphization on the Magnetic Properties of KFeS2 , 1982, April 16.

[26]  Peter G. Wolynes,et al.  Large local energy fluctuations in water. II. Cooperative motions and fluctuations , 1988 .

[27]  Shuichi Iida,et al.  Magnetization Measurements and 55 Mn NMR Studies of LaNi 0.5 Mn 0.5 O 3 , 1979 .

[28]  N. K. Gilra Precrystallization Theory Applied to Ultrasonic Velocity in Supercooled Water , 1967 .

[29]  Aleksandr V. Gurevich,et al.  Self-heating in normal metals and superconductors , 1987 .

[30]  Drago,et al.  Amorphous magnetism in MnxSn , 1988, Physical review. B, Condensed matter.

[31]  S. C. Bhargava,et al.  Mössbauer study of Ni 0.25 Zn 0.75 Fe 2 O 4 . I. Spin fluctuations , 1980 .

[32]  A. Lagar’kov,et al.  Molecular dynamics method in statistical physics , 1978 .

[33]  J. Frankel Kinetic theory of liquids , 1946 .

[34]  V V Slezov,et al.  Diffusive decomposition of solid solutions , 1987 .

[35]  V. Yukalov A method to consider metastable states , 1981 .

[36]  J. Dixmier Les C*-algèbres et leurs représentations .. , 1964 .

[37]  Z. Radovic,et al.  Commensurate-incommensurate phase coexistence in physisorbed monolayers , 1984 .

[38]  E. Nagaev Ferromagnetic and antiferromagnetic semiconductors , 1975 .

[39]  R. Scorzelli,et al.  Magnetic phase present in YBa2(Cu1−xFex)3O6+δ oxides , 1989 .

[40]  R. Micnas,et al.  Superconductivity in narrow-band systems with local nonretarded attractive interactions , 1990 .

[41]  I. M. Fishman FROM THE CURRENT LITERATURE: Steady-state and transient nucleation of a new phase in a first-order transition , 1988 .

[42]  R. J. Wijngaarden,et al.  New Low-Temperature Phase of Molecular Deuterium at Ultrahigh Pressure , 1981 .

[43]  V. Yukalov Quantum crystal with jumps of particles , 1977 .

[44]  H. Matsumoto,et al.  Thermo Field Dynamics and Condensed States , 1982 .

[45]  K. Endō,et al.  NMR study of CsCl-type CoTi1-xAlx , 1983 .

[46]  D. Haar Lectures on selected topics in statistical mechanics. , 1977 .

[47]  V. Yukalov Renormalization of quasi-hamiltonians under heterophase averaging , 1987 .

[48]  Manuel G. Velarde,et al.  Convective instability: A physicist's approach , 1977 .

[49]  L. Schulman,et al.  Analytic continuation at first-order phase transitions , 1982 .

[50]  G. Burns,et al.  Crystalline ferroelectrics with glassy polarization behavior , 1983 .

[51]  A. Khinchin Mathematical foundations of statistical mechanics , 1949 .

[52]  Vimal Singh,et al.  Perturbation methods , 1991 .

[53]  M. Fisher The theory of equilibrium critical phenomena , 1967 .

[54]  J. Clérouin,et al.  Cooperative phenomena below melting of the one component two-dimensional plasma , 1983 .

[55]  V. Skripov,et al.  Spinodal decomposition (phase transitions via unstable states) , 1979 .

[56]  V. Yukalov Spin-phonon interactions in heterophase ferromagnets , 1989 .

[57]  J. Langer Statistical theory of the decay of metastable states , 1969 .

[58]  Anatolii A. Logunov,et al.  Introduction to axiomatic quantum field theory , 1975 .

[59]  A R Bishop,et al.  Solitons in Condensed Matter Physics , 1979 .

[60]  V. Yukalov Microscopic theory of spin reorientations : general analysis , 1990 .

[61]  Jan Leonard van Hemmen,et al.  Statistical-mechanical formalism for spin-glasses , 1984 .

[62]  Cohen,et al.  Spectral shapes of Mössbauer absorption and incoherent neutron scattering from harmonically bound nuclei in Brownian motion: Applications to macromolecular systems. , 1985, Physical review. A, General physics.

[63]  Yoshinori Takahashi,et al.  Spin fluctuations in itinerant electron magnetism , 1985 .

[64]  Polina S. Landa,et al.  Stochastic and Chaotic Oscillations , 1992 .

[65]  G. E. Duvall,et al.  Phase transitions under shock-wave loading , 1977 .

[66]  R. Balescu Equilibrium and Nonequilibrium Statistical Mechanics , 1991 .

[67]  Y. Tret’yakov,et al.  Magnetic semiconductors - Chalcogenide Spinels , 1981 .

[68]  V. Yukalov Statistical theory of heterophase fluctuations , 1981 .

[69]  N. K. Gilra Homogeneous nucleation temperature of supercooled water , 1968 .

[70]  Werner Horsthemke,et al.  Noise-induced transitions , 1984 .

[71]  G. N. Bochkov,et al.  New aspects in 1/ f noise studies , 1983 .

[72]  F. Stillinger,et al.  Quantum statistics and cooperative phenomena , 1965 .

[73]  R. Bullough,et al.  Solitons in Laser Physics , 1979 .

[74]  F. Waldner,et al.  Observation of Excitation of the Antiferromagnetic Mode in the Paramagnetic State of (C 2 H 5 NH 3 ) 2 CuCl 4 , 1978 .

[75]  J. Neumann Mathematical Foundations of Quantum Mechanics , 1955 .

[76]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[77]  Cox,et al.  Structural phase transformations and superconductivity in La2-xBaxCuO4. , 1989, Physical review letters.

[78]  Y. Adda,et al.  Nouveau mécanisme de diffusion dans les solides à haute température , 1987 .

[79]  I. A. Privorotskii THERMODYNAMIC THEORY OF FERROMAGNETIC DOMAINS , 1973 .

[80]  N. Bogolyubov,et al.  Asymptotic Methods in the Theory of Nonlinear Oscillations , 1961 .

[81]  J. K. Srivastava,et al.  On anomalous Mössbauer spectra in spinel ferrites , 1984 .

[82]  Ilya Prigogine,et al.  From Being To Becoming , 1980 .

[83]  V. Yukalov Inversion-polariton Filamentation in Laser Media , 1988 .

[84]  R. K. Pathria,et al.  THEORY OF PHASE TRANSITIONS , 1972 .

[85]  O. Bratteli Operator Algebras And Quantum Statistical Mechanics , 1979 .

[86]  M. Koizumi,et al.  Magnetic phase transition in (Mn0.95Ni0.05)3B4 , 1983 .

[87]  S. V. Sinitsin,et al.  57Fe Mössbauer effect studies of spinreorientational transitions near the compensation point in Y1.6Gd1.4Fe5O12 , 1986 .

[88]  J. Gillis,et al.  Probability and Related Topics in Physical Sciences , 1960 .

[89]  Hideki Tanaka,et al.  Large local energy fluctuations in water , 1987 .

[90]  J. Jortner,et al.  ELECTRONIC STRUCTURE AND TRANSPORT IN LIQUID TE. , 1976 .

[91]  John S. Nicolis,et al.  Dynamics of Hierarchical Systems , 1986 .

[92]  Paul Adrien Maurice Dirac,et al.  Lectures on Quantum Field Theory , 1969 .

[93]  T. D. Cheung,et al.  Spin-glass-like distribution of interaction fields in Ni-Cu alloys , 1981 .

[94]  V. Yukalov Inversion-polarization Filaments under Weak Pumping , 1990 .

[95]  J. Lynn Temperature dependence of the magnetic excitations in iron , 1975 .

[96]  G. Toulouse,et al.  Coexistence of Spin-Glass and Ferromagnetic Orderings , 1981 .

[97]  Blinc,et al.  Cluster distribution in paraelectric KH2AsO4. I. Dispersion of the proton spin-lattice relaxation time. , 1986, Physical review. B, Condensed matter.

[98]  B. A. Huberman,et al.  Peierls state far from equilibrium , 1978 .

[99]  S. V. Sinitsin,et al.  57Fe Mössbauer effect studies of the point defects structure in fast neutron irradiated garnet ferrites Y3Fe5−xAlxO12 , 1986 .

[100]  Nicolas Bourbaki,et al.  Théorie des ensembles , 1954 .

[101]  V. Yukalov Spontaneous restoration of broken symmetry , 1981 .

[102]  David Montgomery,et al.  Two-Dimensional Turbulence , 2012 .

[103]  Alex Hubert,et al.  Theorie der Domänenwände in geordneten Medien , 1974 .

[104]  Neuhaus,et al.  Experimental evidence for spatial inhomogeneous spin freezing in CuMn. , 1985, Physical review. B, Condensed matter.

[105]  S. Kaul Critical phenomena and giant superparamagnetic moments above Curie point of the amorphous Fe 20 Ni 60 P 14 B 6 alloy , 1981 .

[106]  J. Staudenmann The electron charge distribution in V3Si , 1978 .

[107]  A. Bishop,et al.  Mean field and exact results for structural phase transitions in one-dimensional and very anisotropic two-dimensional and three-dimensional systems , 1975 .

[108]  E. T. Jaynes,et al.  Methods of statistical physics , 1981 .

[109]  A. Fetter,et al.  Quantum Theory of Many-Particle Systems , 1971 .

[110]  Morrell H. Cohen,et al.  Inhomogeneous Transport Regime in Disordered Materials , 1973 .

[111]  Vogt,et al.  Coexistence of different short-range-ordered spin fluctuations in Ce1-x(La,Y)xSb. , 1985, Physical review letters.

[112]  D. Haar,et al.  Elements of Thermodynamics , 1966 .

[113]  M. Mehring,et al.  NMR Observation of Static Low-Temperature Clusters above the Phase Transition in the H-Bonded Antiferroelectric Squaric Acid (C4O4H2) , 1979 .

[114]  R. L. Stratonovich,et al.  Nonlinear Nonequilibrium Thermodynamics II , 1992 .

[115]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[116]  John L. Moll,et al.  Physics of Semiconductors , 1964 .

[117]  H. Suzuki,et al.  Local ordering and magnetic properties of disordered Au4Mn and Cu3Mn alloys , 1983 .

[118]  Jacobson,et al.  Anomalous ultrasound propagation in the high-Tc superconductors: La1.8Sr0.2CuO4-y and YBa2Cu3O7- delta. , 1988, Physical review. B, Condensed matter.

[119]  D. Exerowa,et al.  Hole-mediated stability and permeability of bilayers , 1986 .

[120]  B. Rainford,et al.  Inhomogeneous ferromagnetic ordering in Pd Fe and Pd Mn alloys studied via small-angle neutron scattering , 1980 .

[121]  M. Silbert The Molten State of Matter , 1979 .

[122]  René Thom,et al.  Structural stability and morphogenesis , 1977, Pattern Recognit..

[123]  R. Nicklow,et al.  Temperature dependence of the magnetic excitations in Gd , 1981 .

[124]  Morrell H. Cohen,et al.  Conduction regimes in expanded liquid mercury , 1974 .

[125]  C. M. Bastuscheck,et al.  Magnetic behavior of a superconductor--normal-conductor composite SN/sub x/ , 1981 .

[126]  L. Tanner,et al.  Electron microscopy observations of pretransition effects in alloys , 1990 .

[127]  D. Haar Foundations of Statistical Mechanics , 1955 .

[128]  J. C. Phillips,et al.  Physics of High-Tc Superconductors , 1989, Modern Aspects of Superconductivity.

[129]  O. Liechti,et al.  Rb0.22(ND4)0.78D2PO4における常誘電‐反強誘電転移の87Rb‐NMR研究 , 1987 .

[130]  R. Hosemann,et al.  Paracrystalline microdomains in monatomic liquids. II. Three-dimensional structure of microdomains in liquid lead , 1976 .

[131]  Louis Michel,et al.  SYMMETRY DEFECTS AND BROKEN SYMMETRY. CONFIGURATIONS - HIDDEN SYMMETRY , 1980 .

[132]  Grégoire Nicolis,et al.  Self-Organization in nonequilibrium systems , 1977 .

[133]  M. Klinger Self-trapped electron and hole states , 1985 .

[134]  C. Preston Gibbs States on Countable Sets , 1974 .

[135]  L. Gunther Temperature fluctuations and a new third law of thermodynamics , 1989 .

[136]  S. H. Liu Magnetic excitations above the critical temperature , 1976 .

[137]  I. Z. Fisher,et al.  Statistical theory of liquids , 1964 .

[138]  D. Rasmussen,et al.  Clustering in supercooled water , 1973 .

[139]  H. Glättli,et al.  21. Nuclear Magnetism , 1987 .

[140]  Viktor Nikolayevich Popov Functional Integrals in Quantum Field Theory and Statistical Physics , 1983 .

[141]  J. Garland,et al.  Giant-moment clusters in paramagnetic and weakly ferromagnetic Pd-Ni alloys , 1981 .

[142]  Shang‐keng Ma Modern Theory of Critical Phenomena , 1976 .

[143]  S. Ono,et al.  Molecular Theory of Surface Tension in Liquids , 1960 .

[144]  Jacobson,et al.  Elastic anomalies and phase transitions in high-Tc superconductors. , 1988, Physical review letters.

[145]  J. Birman Selection rules for symmetry breaking and symmetry restoration in continuous transitions , 1982 .

[146]  John S. Rowlinson,et al.  New Model for the Study of Liquid–Vapor Phase Transitions , 1970 .

[147]  V. K. Mel'nikov,et al.  Integration method of the Korteweg-de Vries equation with a self-consistent source , 1988 .

[148]  M. Kac Foundations of Kinetic Theory , 1956 .

[149]  Superfluidity of helium II near the λ point , 1976 .

[150]  L. Faddeev,et al.  Hamiltonian Approach to Soliton Theory , 1986 .

[151]  Takanori Saito,et al.  Coexistence of Nonmagnetic and Magnetic Co in Cubic Laves Phase Compounds Lu(Co1-xAlx)2 , 1987 .

[152]  D. Ter Haar,et al.  Elements of Statistical Mechanics , 1954 .

[153]  C. Gardiner Handbook of Stochastic Methods , 1983 .

[154]  Vadim Malyshev,et al.  Gibbs Random Fields , 1991 .

[155]  W. Pickett Electronic structure of the high-temperature oxide superconductors , 1989 .

[156]  D. Rancourt Pervasiveness of cluster excitations as seen in the Mössbauer spectra of magnetic materials , 1988 .

[157]  Hiroshi Watanabe,et al.  Mössbauer Effect Study of Spin Relaxation in CaFe2O4 , 1968 .

[158]  J. Brookeman,et al.  Pretransitional clusters and heterophase fluctuations at first-order phase transitions in crystals , 1981 .

[159]  V. M. Maksimov,et al.  THE PROBLEM OF SYMMETRY BREAKING AND IN VARIANCE OF THE VACUUM IN QUANTUM FIELD THEORY , 1971 .

[160]  D. A. Usikov,et al.  REVIEWS OF TOPICAL PROBLEMS: Minimal chaos, stochastic webs, and structures of quasicrystal symmetry , 1988 .

[161]  H. Mook,et al.  Nature of the magnetic excitations above Tc in Ni and Fe , 1986 .

[162]  V. Yukalov Heterophase fluctuations in ferroelectrics , 1988 .

[163]  Hermann Haken,et al.  Laser light dynamics , 1985 .

[164]  A. Bruce,et al.  Structural phase transitions , 1981 .

[165]  É. L. Nagaev Physics of Magnetic Semiconductors , 1984 .

[166]  Micklitz,et al.  Dynamical information for Fe-doped YBa2Cu3O7 superconducting oxides obtained from high-temperature Mössbauer studies. , 1990, Physical review. B, Condensed matter.

[167]  H. Mook,et al.  Temperature dependence of the dynamic susceptibility of nickel , 1981 .

[168]  N. N. Bogolyubov,et al.  Problems of a Dynamical Theory in Statistical Physics , 1959 .

[169]  L. Ballentine,et al.  Probabilistic and Statistical Aspects of Quantum Theory , 1982 .

[170]  Charles E. Johnson,et al.  The Mössbauer effect and magnetic phase transitions , 1989 .

[171]  R. Weinstock New Approach to Statistical Mechanics , 1967 .

[172]  G. Volovik Superfluid properties of 3He-A , 1984 .

[173]  Z. Fisk,et al.  Low temperature phase transitions and magnetic structure of PrB6 , 1980 .

[174]  L. Pastur,et al.  Introduction to the Theory of Disordered Systems , 1988 .

[175]  J. R. Schrieffer,et al.  Dynamics and statistical mechanics of a one-dimensional model Hamiltonian for structural phase transitions , 1974 .

[176]  M. Date,et al.  Coexistence of ferromagnetic and nonmagnetic Co in CoTi1−xAlx and CoTi1−yGay , 1983 .

[177]  R. G. Pillay,et al.  Novel behaviour of iron moments in new magnetic systems RuFeSi and RuFeB , 1983 .

[178]  J. R. Schrieffer Theory of Superconductivity , 1965 .

[179]  B. Smirnov,et al.  Metastable magnetic crystals , 1976 .

[180]  G. Agarwal Quantum statistical theories of spontaneous emission and their relation to other approaches , 1974 .

[181]  V. Yukalov Procedure of quasi-averaging for heterophase mixtures , 1987 .

[182]  Rudolf Peierls,et al.  Surprises in Theoretical Physics , 1981 .

[183]  J. Genossar,et al.  Precursor order clusters at ferroelectric phase transitions , 1984 .

[184]  Katherine J. Strandburg,et al.  Two-dimensional melting , 1988 .

[185]  F. H. Dacol,et al.  Glassy polarization behavior in ferroelectric compounds Pb(Mg13Nb23)O3 and Pb(Zn13Nb23)O3 , 1983 .

[186]  H. Araki,et al.  On the dynamics and ergodic properties of theXY model , 1983 .

[187]  T. Goto,et al.  Coexistence of nonmagnetic and ferromagnetic Co in Y2Co7 and YCo3 hydrides , 1986 .

[188]  V. Aksenov,et al.  Neutron scattering by ferroelectrics , 1990 .

[189]  J. Tuszynski,et al.  Exact solutions to the time-dependent Landau-Ginzburg model of phase transitions , 1984 .

[190]  Gérard G. Emch,et al.  Algebraic methods in statistical mechanics and quantum field theory , 1972 .

[191]  J. Suchanicz,et al.  Electrostrictive strain and pyroeffect in the region of phase coexistence in Na0.5Bi0.5TiO3 , 1988 .

[192]  V. Yukalov Lattice mixtures of fluctuating phases , 1987 .

[193]  A. C. Zettlemoyer,et al.  Homogeneous Nucleation Theory , 1974 .

[194]  M. Anisimov Critical phenomena in liquids and liquid crystals , 1991 .

[195]  Joel Keizer,et al.  Statistical Thermodynamics of Nonequilibrium Processes , 1987 .

[196]  P. Chieux Small angle neutron scattering studies of concentration fluctuations in the non metal to metal transition range: solutions of 7Li in ND3 , 1974 .

[197]  P. Leath,et al.  The theory and properties of randomly disordered crystals and related physical systems , 1974 .

[198]  Ya. B. Zel'Dovich,et al.  Intermittency in random media , 1987 .

[199]  K. Wilson The renormalization group: Critical phenomena and the Kondo problem , 1975 .

[200]  A. Lichtenberg,et al.  Regular and Stochastic Motion , 1982 .

[201]  R. Feynman,et al.  Quantum Mechanics and Path Integrals , 1965 .

[202]  V. Yukalov Remarks on quasiaverages , 1976 .

[203]  A. Larkin,et al.  On Phase Transitions of Second Order , 1966 .

[204]  P. Tseng,et al.  Mössbauer-effect studies on the magnetic properties of the Ni-Zn—ferrite system , 1982 .

[205]  N. Bogolubov,et al.  Introduction to quantum statistical mechanics , 1982 .

[206]  Michael E. Fisher,et al.  The renormalization group in the theory of critical behavior , 1974 .

[207]  J. I. Spielberg,et al.  Further studies on the molecular dynamics of the glass transition and the glass state using EPR probes , 1984 .

[208]  D. Ter Haar,et al.  THEORY AND APPLICATIONS OF THE DENSITY MATRIX , 1961 .

[209]  V. Yukalov Model of a hybrid crystal , 1976 .

[210]  Cable,et al.  Spin dynamics of Gd at high temperatures. , 1989, Physical review. B, Condensed matter.

[211]  P. Hohenberg,et al.  Theory of Dynamic Critical Phenomena , 1977 .

[212]  R. Mints,et al.  Localized waves in inhomogeneous media , 1984 .

[213]  N. B. Kopnin,et al.  Theory of current states in narrow superconducting channels , 1984 .

[214]  F. Borsa,et al.  Diffusion and Phononlike Excitations in Intercalated Graphite from 133 Cs NMR and Relaxation , 1984 .

[215]  N. Dass,et al.  Precrystallisation Theory Applied to Surface-Free Energy of the Water-Ice Interface , 1968 .

[216]  D. C. Spanner,et al.  Introduction to Thermodynamics , 1964 .

[217]  K. Binder,et al.  Spin glasses: Experimental facts, theoretical concepts, and open questions , 1986 .

[218]  John Formby,et al.  An introduction to the mathematical formulation of self-organizing systems , 1968 .

[219]  U. Enz,et al.  Dynamic properties of magnetic domain walls and magnetic bubbles , 1980 .

[220]  S. Gurbatov,et al.  REVIEWS OF TOPICAL PROBLEMS: Nonlinear waves and one-dimensional turbulence in nondispersive media , 1983 .

[221]  G. Iooss,et al.  Elementary stability and bifurcation theory , 1980 .

[222]  N. Dass,et al.  Refractive Index of Liquids on Supercooling-Water , 1966 .

[223]  R. Apfel,et al.  The sound velocity in metastable liquid water under atmospheric pressure , 1978 .

[224]  T. Schneider,et al.  Molecular-dynamics study of structural-phase transitions. I. One-component displacement models , 1976 .

[225]  H. Walther,et al.  Phase transitions of stored laser-cooled ions , 1988, Nature.

[226]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[227]  H. Mori A Quantum-statistical Theory of Transport Processes , 1956 .

[228]  M. Weissman 1/f noise and other slow, nonexponential kinetics in condensed matter. , 1988 .

[229]  Vladimir I. Emel'yanov,et al.  Collective spontaneous emission (Dicke superradiance) , 1980 .

[230]  James D. Gunton,et al.  Introduction to the Theory of Metastable and Unstable States , 1983 .

[231]  A. Shumovsky,et al.  Lectures on phase transitions , 1990 .

[232]  F. Wanderlingh,et al.  Evidence of anomalous acoustic behavior from Brillouin scattering in supercooled water , 1984 .

[233]  Chandra Anomalous volume expansion in Hg1-xCdxTe melts: An analysis employing the inhomogeneous structure model. , 1985, Physical review. B, Condensed matter.

[234]  P. Landa,et al.  METHODOLOGICAL NOTES: Self-oscillatory systems with high-frequency energy sources , 1989 .

[235]  W. Abdul-Razzaq,et al.  Spin glassiness and ferromagnetism in disordered Ni‐Mn (invited) , 1984 .

[236]  Neville H Fletcher,et al.  The Chemical Physics of Ice , 1970 .

[237]  Y. Hiwatari Free volumes and liquidlike clusters in soft‐core dense liquids and glasses , 1982 .

[238]  V. Yukalov Effective Hamiltonians for systems with mixed symmetry , 1986 .