Lecture 2 - Purdue Physics
... EM fields are real physical substance Electromagnetic fields are real, these are not just mathematical concepts. EM fields is another material substance: one can assign energy-density to electromagnetic field. Empty space with EM field has more energy than just empty space. There is no “substan ...
... EM fields are real physical substance Electromagnetic fields are real, these are not just mathematical concepts. EM fields is another material substance: one can assign energy-density to electromagnetic field. Empty space with EM field has more energy than just empty space. There is no “substan ...
Finite-difference time-domain simulation of thermal noise in open
... structures, the required information of modes is unknown a priori. Thus it is desirable to be able to study the noise of a cavity field without prior knowledge of cavity modes. Additional problems with the modal picture are as follows. 共i兲 If the cavity is very leaky, the significant overlap of mode ...
... structures, the required information of modes is unknown a priori. Thus it is desirable to be able to study the noise of a cavity field without prior knowledge of cavity modes. Additional problems with the modal picture are as follows. 共i兲 If the cavity is very leaky, the significant overlap of mode ...
Lecture Notes in Statistical Mechanics and Mesoscopics Thermal
... a wavepacket in the case of a non-linear oscillator. In such case V (x) has either sub-quadratic or super-quadratic variation, and consequently the oscillation frequency ω(E) depends on the energy: decreases or increases with energy respectively. If the initial distribution has some finite spread σE ...
... a wavepacket in the case of a non-linear oscillator. In such case V (x) has either sub-quadratic or super-quadratic variation, and consequently the oscillation frequency ω(E) depends on the energy: decreases or increases with energy respectively. If the initial distribution has some finite spread σE ...
Physics
... infer impulse as product of impulsive force and time; describe law of conservation of momentum; apply law of conservation of momentum and study the special cases of elastic collision between two bodies in one dimension; describe the force produced due to flow of water; apply the law of conservation ...
... infer impulse as product of impulsive force and time; describe law of conservation of momentum; apply law of conservation of momentum and study the special cases of elastic collision between two bodies in one dimension; describe the force produced due to flow of water; apply the law of conservation ...
4.2 極化物體的場(The Field of a Polarized Object)
... When we calculate the electric fields and potential via bound charges, we obtain the “macroscopic” field. the “macroscopic” field : the average field over regions large enough to contain many thousands of atoms. Ordinarily, the macroscopic field is what people mean when they speak of “the” field ins ...
... When we calculate the electric fields and potential via bound charges, we obtain the “macroscopic” field. the “macroscopic” field : the average field over regions large enough to contain many thousands of atoms. Ordinarily, the macroscopic field is what people mean when they speak of “the” field ins ...
SEMICLASSICAL AND LARGE QUANTUM NUMBER LIMITS
... wells which go to infinity as some positive power of the coordinate r at large distances. Potential wells converging to a constant, e.g. zero, on at least one side can support an infinite number of bound states, if the potential approaches its limiting threshold value slower than 1/r2 , as is the ca ...
... wells which go to infinity as some positive power of the coordinate r at large distances. Potential wells converging to a constant, e.g. zero, on at least one side can support an infinite number of bound states, if the potential approaches its limiting threshold value slower than 1/r2 , as is the ca ...
Casimir effect
In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. They are named after the Dutch physicist Hendrik Casimir.The typical example is of two uncharged metallic plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured and is a striking example of an effect captured formally by second quantization. However, the treatment of boundary conditions in these calculations has led to some controversy.In fact, ""Casimir's original goal was to compute the van der Waals force between polarizable molecules"" of the metallic plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) of quantum fields.Dutch physicists Hendrik B. G. Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947, and, after a conversation with Niels Bohr who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948; the former is called the Casimir–Polder force while the latter is the Casimir effect in the narrow sense. Predictions of the force were later extended to finite-conductivity metals and dielectrics by Lifshitz and his students, and recent calculations have considered more general geometries. It was not until 1997, however, that a direct experiment, by S. Lamoreaux, described above, quantitatively measured the force (to within 15% of the value predicted by the theory), although previous work [e.g. van Blockland and Overbeek (1978)] had observed the force qualitatively, and indirect validation of the predicted Casimir energy had been made by measuring the thickness of liquid helium films by Sabisky and Anderson in 1972. Subsequent experiments approach an accuracy of a few percent.Because the strength of the force falls off rapidly with distance, it is measurable only when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of about 1 atmosphere of pressure (the precise value depending on surface geometry and other factors).In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics, it is significant in some aspects of emerging microtechnologies and nanotechnologies.Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string as well as plates submerged in noisy water or gas illustrate the Casimir force.