Physical model

Drude model, where independent electrons, in blue, follow the gradient of the electric field, and crash against rigid ions, in red.

A physical model can refer to a theoretical construction (mathematical model) of a physical system. Also to a montage with real objects that reproduce the behavior of some aspects of a more complex physical or mechanical system at a different scale (miniature material model). The term appears with different meanings in the field of physics or in that of applied physics, such as engineering.

In physics

A certain physical theory is said to be a model or a theoretical physical model when its internal dynamics (the basic laws of temporal evolution that are determined by the Hamiltonian) they are not exactly known. Or when they are known but, if what is sought is to study exclusively some particular details of a complex system, it may be profitable (technically) to use another type of (fictitious) dynamics that makes the behavior under study of the complete system approximately the same as the one you would have with the most complicated dynamics.

These models are applied in all areas of physics (meteorology, thermodynamics, nuclear physics, materials, etc.) except theoretical physics. Like any physical theory, such a model, by reducing observed behavior to more basic fundamental facts, helps to explain and predict the behavior of a physical system under various circumstances. However, because it is not based on a fundamentally correct description, the model is expected to fail outside its field of application.

Model Hamiltonian

Theoretical physical models are sometimes expressed in the form of an effective Hamiltonian or model Hamiltonian that The Hamiltonian does not explicitly consider all system variables, but rather summarizes them into a small number of interactions. Although their eigenfunctions contain only a small part of the information necessary for a complete description, it is sought that the differences between their eigenvalues correspond exactly to the differences between the real energies, so they can be used to rationalize experimentally measured properties. Its objective is commonly a simplified description of the problem, in which the effect of a specific phenomenon is rigorously studied, using an implicit description of the rest of the phenomena. Strictly speaking, there are subtle differences between the effective Hamiltonians and the model Hamiltonians, derived from the way of parameterizing the interactions. Model Hamiltonians are used as an auxiliary tool in a wide range of fields of physics, including condensed matter physics, optics, and nuclear physics.

The use of effective Hamiltonians, as opposed to complete quantum Hamiltonians, has the main advantage of making the system more intuitively understandable, since it is easier to reason and propose theoretical models using parameterized interactions. On the other hand, it is possible to work with much larger systems, since full quantum calculations are much more computationally expensive. The main disadvantage of effective Hamiltonians is that they themselves lack predictive power: they have to rely on external experimental data (or rigorous calculations) to estimate parameter values.

In the description of magnetic compounds, effective hamiltonians are commonly used instead of, for example, the complete molecular hamiltonian, which includes a lot of chemical information that is irrelevant to the description of magnetic properties. For example, it is spoken of hamiltonians of thorn to describe phenomena as varied as the field of ligants, the magnetic exchange, the sphin-orbit coupling, the null field depopulation, the Zeeman effect, the hyperphine structure or the vibronic coupling. Indeed, the main operators included in these hamiltonians only depend on spinal variables, such as S{displaystyle S}, Sz{displaystyle S_{z}} and/or S2{displaystyle S^{2}}.

Practical physical model

On the other hand, a practical physical model is a concrete material realization, with which it is not necessarily intended to build a theory but rather to expand the set of observed facts that can be used to confirm or reformulate the theories. These practical physical models are the subject of experiments on which they broaden the base of observed facts. In physics, practical physical models are only an intermediate step towards the formulation of theoretical physical models, which in turn are the basis of physical theories.

In engineering

In engineering, physical models, as opposed to mathematical models and analog models, are normally constructions on a reduced or simplified scale of works, machines or engineering systems to study their behavior and thus allow the designs to be perfected, before to start the construction of real works or objects. For this reason, this type of model is also often called a reduced model or a simplified model.

They are frequently used for the study of dams, bridges, locks, ports, aircraft in wind tunnels, etc. Many times, for complex works, such as a dam, the construction of more than one model may be required. In this example, it is customary to study a general model of the layout of the dam, with all its parts, a specific model on a larger scale for the spillway and the dissipation basin, another for the intake(s), and a different one for the discharge of bottom.

⊂== See also ==⊃

• Physics
• Creation of simulation models with System Dynamics
• Similar model
• Scientific model
• Mental model
• Simulation