Glossary: General physics, statistical and condensed matter physics

1. coarse-graining: replacement of microscopic variables by average variables on an expanded length scale (with an upper wave number cutoff).

2. coexistence: simultaneous equilibrium of two or more distinct thermodynamic phases, e.g., water and vapor are in equilibrium on the liquid-gas coexistence line.

3. commensurate lattice: lattice that can be divided into two or more sublattices, each of whose basis vectors is a rational multiple of the basis vectors of the other sublattices. Contrast with incommensurate lattice.

4. complex fluid: opposed to simple fluid; non-newtonian fluid characterized by intricate visco-elastic rheological behavior.

5. conjugate variable: The work done in changing an extensive thermodynamic variable is the product of the change in that variable and its conjugate intensive variable. Thus volume and pressure are conjugate variables, as are particle number and chemical potential.

6. critical point: point in a phase diagram characterized by singularities in derivatives of the free energy and related thermodynamic quantities.

7. critical slowing down: slowing down of dynamical processes at a second-order critical point. The dynamical slowing down is described by a dynamical critical exponent, z, in addition to static exponents such as &nu or &gamma .

8. correlation length
9. direct lattice: a lattice of points in coordinate (as opposed to reciprocal) space.

10. ensemble:

11. ergodicity: Boltzmann's ergodicity hypothesis states that time and ensemble averages are equivalent if the total phase space is connected and can be explored by the system and if, in addition, sufficiently time is given that the system is able to do this.

12. excluded volume: In systems that are dominated by entropy the effect of short-range potentials can be treated in terms of the reduction in available volume produced by a nonzero density of particles. In a hard-sphere gas, the reduced or excluded volume for N particles of volume b is N b, and the entropy of such a gas confined to a container of volume V is N ln(V-Nb). The entropic effects are much more interesting in the case of polymers where a random walk becomes a self-avoiding random walk in the presence of monomer excluded volume effects. ^{[ G79, DE86 ]} This changes the dependence of the size of a polymer on the degree of polymerization N from being proportional to N^1/2 to being proportional to N^&nu=3/(d+2) where d is the spatial dimension.

13. fractal
14. Flory theory
15. intensive variable: a thermodynamic variable that remains unchanged when the system is doubled (or tripled etc.) in size. Examples are pressure, temperature, and chemical potential. Extensive variables, such as free energies, entropy, number of particles, and volume can be made intensive by dividing by the volume (to make energy density, etc.).

16. mesoscopic scale: 10³-10⁵nm

17. n-vector model: important general model in statistical physics

18. order parameter: parameter distinguishing an ordered from a disordered phase. For example, the order parameter for a ferromagnet is the average magnetization m. It is zero in the high-temperature paramagnetic phase where spins are randomly oriented and nonzero in the ferromagnetic phase where spins align on average along a common direction.

19. persistence length: the correlation length for unit tangent vectors to a polymer or unit normals to a surface, i.e., the distance over which the object is effectively linear or flat.

20. random walk (RW): A series of uncorrelated steps of average step length a describe a random path with zero average displacement but characteristic size (as measured by the radius of gyration or the end-to-end length) proportional to square root of the number of steps N. The Haussdorf dimension of the random walk is 2. The probability of return to the origin for an infinite random walk is 1 in one or two dimensions but is less than 1 in dimensions greater than 2 (i.e., for d>2, there is a nonzero probability of escape or equivalently of not returning to the origin).

21. relaxation time &tau: time equilibrium fluctuations need to relax. The relaxation time of a polymer chain is (normally) given by the time the chain needs to diffuse over its own size R. For strongly entangled polymer melts this implies an increase of the relaxation time (at least) as the cube of the chain length N.

22. renormalization group (RG): a transformation involving thinning of degrees of freedom (coarse-graining), coupled with a change in length scale. For example, representing a group of spins as a block spin and the constructing a Hamiltonian on the scale of the block spins.

23. ... (RISM):

24. self-similar: a structure that "looks the same" at all length scales. Its correlation functions have no characteristic length and therefore are typically power laws with distance or wave vector.

25. soft matter: Roughly speaking, soft matter consists of materials whose constituents have a mesoscopic size (10³-10⁵nm) for which k_BT is the important energy scale (whence the softness at ambient conditions). Examples are polymers, colloidal suspensions, liquid crystals, or fluid membranes.

26. spinodal curve: curve separating metastable from unstable regions in the coexistence regions of binary fluids. A spinodal decomposition process is a decay towards equilibrium in a locally unstable region of a phase diagram constrained by particle conservation. This is typically seen in quenches of binary mixtures. The decay to equilibrium above the spinodal curve is via droplet nucleation, decay below the spinodal curve is via the formation of initially small amplitude periodic modulations of the order parameter.

27. stochastic variable: a variable which changes with time such that there is no correlation between different time intervals. A random variable.

28. topology: consequence of the impossibility of the chains to cross. Important for ring polymers and other architectures containing closed loops. The knotted DNA ring ("plasmon") on the right is, for instance, in a different topological class as an open unknotted ring.

29. universality: Due to there large size polymer chains may be (often) described in terms of few effective coefficients (e.g., the excluded volume parameter v or the Flory-Huggins parameter &Chi) and/or exponents (e.g., the Flory exponent &nu). Chemical details may change the coefficients without changing the overall physical behavior. More general, the idea of universality means that different physical systems are described by generic models with the same characteristic exponents. For instance, dilute linear homopolymer chains in the good solvent fall in the same class of models as the n &rArr 0 limit of the n-vector model.