Physical Systems

Hermann Haken

K. Kong Wan

A physical theory aims to give a description of the properties and behaviour of a physical system, both qualitatively and quantitatively. Qualitatively a theory should explain the behaviour of a given physical system in terms of some fundamental properties of the system. The study of the mathematical aspects of theoretical physics is often referred to as mathematical physics. Apart from the requirement of mathematical consistency, a theory is judged by how well its predictions agree with empirical observations, especially by its ability to make new and experimentally verifiable predictions. A physical system possesses many physical quantities which reflect the properties of the system. A physical quantity is a property of the system which can be physically observed and measured to yield numerical values. To emphasise their measurability, these quantities are called observables. The relationship between states and observables can be complicated, depending on whether we are dealing with classical systems or quantum systems.

Bernard d’Espagnat

Classical and quantum physics both make considerable use of the expressions "physical system" and "state of a physical system." Indeed, any sufficiently isolated thing—a voltmeter, an electron, or a molecule—is a physical system. The expression physical system is taken in its familiar, intuitive sense. For instance, a partially but sufficiently isolated atom is a physical system or, for short, a system. This chapter summarizes the rules of quantum mechanics. Quantum mechanics is essentially a statistical theory. Except in special cases it makes no prediction that bears on individual systems. The observables which have a continuous eigenvalue spectrum have eigenvectors that are not normalizable. As regards the measurement of these observables, some technical changes should therefore be made in expression. The chapter introduces vector space which has the structure of a Hilbert space for describing ensembles of physical systems of the same type.

Hermann Haken

Indrani Bose

This chapter focuses on the physical basis of some integrable spin models in condensed matter physics and the useful physical insights derived from the solution of these models. The antiferromagnetic ground state serves as the physical vacuum for the creation of elementary excitations. The study of integrable models constitutes an important area of theoretical physics. Integrable models in condensed matter physics describe interacting many-particle systems. The most prominent examples are interacting spin and electron systems which include several real materials of interest. Integrable models, because of their exact solvability, provide a complete and unambiguous understanding of the variety of phenomena exhibited by real systems. Integrable models are sometimes more general than what is necessary to describe real systems. A major portion of the review is devoted to physical systems which exhibit rich phenomena, like the systems with both spin and orbital degrees of freedom and undoped and doped spin ladder systems, where the need for integrable systems is particularly strong.

Walter E Thirring