We introduce a flexible string model of the hydrocarbon chain and derive an analytical expression for the lateral pressure profile across the hydrophobic core of the membrane. The pressure profile influences the functioning of the embedded proteins and is difficult to measure experimentally. In our model the hydrocarbon chain is represented as a flexible string of finite thickness with a given bending rigidity. In the mean-field approximation we substitute the entropic repulsion between neighboring chains in a lipid membrane by an effective potential. The effective potential is determined self-consistently. The arbitrary chain conformation is expanded over eigenfunctions of the self-adjoint operator of the chain energy density. The lateral pressure distribution across the bilayer is calculated using the path integral technique. We found that the pressure profile is mainly formed by the sum of the partial contributions of a few discrete lowest-energy “eigenconformations.” The dependences on temperature and area per lipid of the lateral pressure produced by the hydrocarbon chains are found. We also calculated the chain contribution to the area compressibility modulus and the temperature coefficient of area expansion.

In this work we derive analytically various thermodynamic properties of bolalipid membranes using microscopic model (elastic strings) and path-integral technique. Among calculated characteristics are lateral pressure profile (with and without hairpin bolalipids), chain orientational order parameter, pressure-area isotherms, coefficient of thermal area expansion, compressibility modulus, and area per bolalipid chain as a function of temperature. Results are compared with our previous ones for a monopolar lipid bilayer and with results of other relevant studies. The limiting case of absolutely rigid strings is also considered. Evaluation of quantum effects is made and found to be negligible. DOI: http://dx.doi.org/10.1103/PhysRevE.82.051901 © 2010 The American Physical Society

Quantum batteries, which are quantum systems to be used for the storage and transformation of energy, have been recently attracting research interest. A promising candidate for their investigation is the Dicke model, which describes an ensemble of two-level systems interacting with a single-mode electromagnetic wave in a resonator cavity. In order to charge the battery, a coupling between the ensemble of two-level systems and resonator cavity should be turned off at a certain moment of time. This moment of time is chosen in such a way that the energy gets fully stored in an ensemble of two-level systems. In our previous works we have investigated a bound-luminosity superradiant state of the extended Dicke model and found analytical expressions for the dynamics of coherent energy transfer between the superradiant condensate and the ensemble of two-level systems. Here, using our previous results, we have derived analytically the superlinear law for the quantum battery charging power $P\sim N^{3/2}$ as a function of the number $N$ of two-level systems in the battery, and also the $N$ dependence for the charging time $t_c\sim N^{-1/2}$. The $N$ exponent $3/2$ of the charging power is in quantitative correspondence with the recent result $1.541$ obtained numerically by other authors. The physics of Dicke quantum battery charging is considered in detail.