This book gives an introduction to molecular biophysics. It starts from material properties at equilibrium related to polymers, dielectrics and membranes. Electronic spectra are developed for the understanding of elementary dynamic processes in photosynthesis including proton transfer and dynamics of molecular motors. Since the molecular structures of functional groups of bio-systems were resolved, it has become feasible to develop a theory based on the quantum theory and statistical physics with emphasis on the specifics of the high complexity of bio-systems. This introduction to molecular aspects of the field focuses on solvable models. Elementary biological processes provide as special challenge the presence of partial disorder in the structure which does not destroy the basic reproducibility of the processes. Apparently the elementary molecular processes are organized in a way to optimize the efficiency. Learning from nature by means exploring the relation between structure and function may even help to build better artificial solar cells. The reader is exposed to basic concepts in modern biophysics, such as entropic forces, phase separation, potential of mean force, electron and proton transfer, heterogeneous reactions, coherent and incoherent energy transfer as well as molecular motors. Basic knowledge in classical and Quantum mechanics, electrostatics and statistical physics is desirable. Simplified models are presented which can be solved in limited cases analytically from the guiding lines to generate the basis for a fundamental understanding of the more complex biophysical systems. Chapters close with challenging problems whose solutions are provided at the end of the book to complete the pedagogical treatment in the book. To the second edition several new chapters were added. The medium polarization is treated self-consistently using basic elements of polaron theory and more advanced nonlinear Schroedinger equations to describe the dynamics of solvation. Ion transport through a membrane was extended by the discussion of cooperative effects. Intramolecular transitions are now discussed in the new edition in much more detail, including also radiationless transitions. Very recent developments in spectroscopy are included, especially two-dimensional and hole-burning spectroscopy. The discussion of charge transfer processes was extended by including recent results of hole transfer in DNA in connection with the super-exchange mechanism. The chapter on molecular motors was rewritten to include the most recent developments of new models. The book is a useful text for students and researchers wanting to go through the mathematical derivations in the theories presented. This book attracts a group of applied mathematically oriented students and scholars to the exciting field of molecular biophysics.

Biophysics deals with biological systems, such as proteins, which ful?ll a va- ety of functions in establishing living systems. While the biologistuses mostly a phenomenological description, the physicist tries to ?nd the general c- cepts to classify the materials and dynamics which underly speci?c processes. The phenomena span a wide range, from elementary processes, which can be induced by light excitation of a molecule, to communication of living s- tems. Thus, di?erent methods are appropriate to describe these phenomena. From the point of view of the physicist, this may be Continuum Mechanics to deal with membranes, Hydrodynamics to deal with transportthrough vessels, Bioinformatics to describe evolution, Electrostatics to deal with aspects of binding, Statistical Mechanics to account for temperature and to learn about the role of the entropy, and last but not least Quantum Mechanics to und- stand the electronic structure of the molecular systems involved. As can be seen from the title, Molecular Biophysics, this book will focus on systems for which su?cient information on the molecular level is available. Compared to crystallizedstandard materials studied in solid-state physics, the biological systems arecharacterizedby verybig unit cells containingproteinswith th- sands of atoms. In addition, there is always a certain amount of disorder, so that the systems can be classi?ed as complex. Surprisingly, the functions like a photocycle or the folding of a protein are highly reproducible, indicating a paradox situation in relation to the concept of maximum entropy production.

This textbook presents basic numerical methods and applies them to a large variety of physical models in multiple computer experiments. Classical algorithms and more recent methods are explained. Partial differential equations are treated generally comparing important methods, and equations of motion are solved by a large number of simple as well as more sophisticated methods. Several modern algorithms for quantum wavepacket motion are compared. The first part of the book discusses the basic numerical methods, while the second part simulates classical and quantum systems. Simple but non-trivial examples from a broad range of physical topics offer readers insights into the numerical treatment but also the simulated problems. Rotational motion is studied in detail, as are simple quantum systems. A two-level system in an external field demonstrates elementary principles from quantum optics and simulation of a quantum bit. Principles of molecular dynamics are shown. Modern boundary element methods are presented in addition to standard methods, and waves and diffusion processes are simulated comparing the stability and efficiency of different methods. A large number of computer experiments is provided, which can be tried out even by readers with no programming skills. Exercises in the applets complete the pedagogical treatment in the book. In the third edition Monte Carlo methods and random number generation have been updated taking recent developments into account. Krylov-space methods for eigenvalue problems are discussed in much more detail. Short time Fourier transformation and wavelet transformation have been included as tools for time-frequency analysis. Lastly, elementary quantum many-body problems demonstrate the application of variational and Monte-Carlo methods.

This book gives an introduction to molecular biophysics. It starts from material properties at equilibrium related to polymers, dielectrics and membranes. Electronic spectra are developed for the understanding of elementary dynamic processes in photosynthesis including proton transfer and dynamics of molecular motors. Since the molecular structures of functional groups of bio-systems were resolved, it has become feasible to develop a theory based on the quantum theory and statistical physics with emphasis on the specifics of the high complexity of bio-systems. This introduction to molecular aspects of the field focuses on solvable models. Elementary biological processes provide as special challenge the presence of partial disorder in the structure which does not destroy the basic reproducibility of the processes. Apparently the elementary molecular processes are organized in a way to optimize the efficiency. Learning from nature by means exploring the relation between structure and function may even help to build better artificial solar cells. The reader is exposed to basic concepts in modern biophysics, such as entropic forces, phase separation, potential of mean force, electron and proton transfer, heterogeneous reactions, coherent and incoherent energy transfer as well as molecular motors. Basic knowledge in classical and Quantum mechanics, electrostatics and statistical physics is desirable. Simplified models are presented which can be solved in limited cases analytically from the guiding lines to generate the basis for a fundamental understanding of the more complex biophysical systems. Chapters close with challenging problems whose solutions are provided at the end of the book to complete the pedagogical treatment in the book. To the second edition several new chapters were added. The medium polarization is treated self-consistently using basic elements of polaron theory and more advanced nonlinear Schroedinger equations to describe the dynamics of solvation. Ion transport through a membrane was extended by the discussion of cooperative effects. Intramolecular transitions are now discussed in the new edition in much more detail, including also radiationless transitions. Very recent developments in spectroscopy are included, especially two-dimensional and hole-burning spectroscopy. The discussion of charge transfer processes was extended by including recent results of hole transfer in DNA in connection with the super-exchange mechanism. The chapter on molecular motors was rewritten to include the most recent developments of new models. The book is a useful text for students and researchers wanting to go through the mathematical derivations in the theories presented. This book attracts a group of applied mathematically oriented students and scholars to the exciting field of molecular biophysics.