Nucleation rates in flat and curved space

Nucleation rates for tunneling processes in Minkowski and de Sitter space are investigated, taking into account one loop prefactors. In particular, we consider the creation of membranes by an antisymmetric tensor field, analogous to Schwinger pair production. This can be viewed as a model for the decay of a false (or true) vacuum at zero temperature in the thin wall limit. Also considered is the spontaneous nucleation of strings, domain walls, and monopoles during inflation. The instantons for these processes are spherical world sheets or world lines embedded in flat or de Sitter backgrounds. We find the contribution of such instantons to the semiclassical partition function, including the one loop corrections due to small fluctuations around the spherical world sheet. We suggest a prescription for obtaining, from the partition function, the distribution of objects nucleated during inflation. This can be seen as an extension of the usual formula, valid in flat space, according to which the nucleation rate is twice the imaginary part of the free energy. For the case of pair production, the results reproduce those that can be obtained using second quantization methods, confirming the validity of instanton techniques in de Sitter space. Throughout the paper, both the gravitational field and the antisymmetric tensor field are assumed external.

Pair production by and electric field in (1+1)-dimensional de Sitter space

We use the method of Bogolubov transformations to compute the rate of pair production by an electric field in (1+1)-dimensional de Sitter space. The results are in agreement with those obtained previously using the instanton methods. This is true even when the size of the instanton is comparable to the size of the de Sitter horizon.

Heat kernels and thermodynamics in Rindler space

We point out that using the heat kernel on a cone to compute the first quantum correction to the entropy of Rindler space does not yield the correct temperature dependence. In order to obtain the physics at arbitrary temperature one must compute the heat kernel in a geometry with different topology (without a conical singularity). This is done in two ways, which are shown to agree with computations performed by other methods. Also, we discuss the ambiguities in the regularization procedure and their physical consequences.

Singularity-free space-time

We show that the solution published in the paper by Senovilla [Phys. Rev. Lett. 64, 2219 (1990)] is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, the strong energy condition, causal symmetry, and causal stability. A detailed discussion about which assumptions in the singularity theorems are not satisfied is performed, and we show explicitly that the solution is in accordance with those theorems. A brief discussion of the results is given.

Partition coefficient and molecular flexibility: the concept of lipophilicity space.

The rationale of this study was to investigate molecular flexibility and its influence on physicochemical properties with a view to uncovering additional information on the fuzzy concept of dynamic molecular structure. Indeed, it is now known that computed molecular interaction fields (MIFs) such as molecular electrostatic potentials (MEPs) and lipophilicity potentials (MLPs) are conformation-dependent, as are dipole moments. A database of 125 compounds was used whose conformational space was explored, while conformation-dependent parameters were computed for each non-redundant conformer found in the conformational space of the compounds. These parameters were the virtual log P (log P(MLP), calculated by a MLP approach), the apolar surface area (ASA), polar surface area (PSA), and solvent-accessible surface (SAS). For each compound, the range taken by each parameter (its property space) was divided by the number of rotors taken as an index of flexibility, yielding a parameter termed 'molecular sensitivity'. This parameter was poorly correlated with others (i.e., it contains novel information) and showed the compounds to fall into two broad classes. 'Sensitive' molecules are those whose computed property ranges are markedly sensitive to conformational effects, whereas 'insensitive' (in fact, less sensitive) molecules have property ranges which are comparatively less affected by conformational fluctuations. A pharmacokinetic application is presented.