❤️ Saint Columba (disambiguation) ✨

"Saint Columba (521–597) was an Irish Christian saint who evangelized Scotland. Saint Columba may also refer to: Saints * Columba of Cornwall or Saint Columba the Virgin * Columba of Sens * Columba of Spain * Columba of Terryglass Schools * St. Columba's College, Hazaribagh, India * St Columba's College, Dublin, a co-educational boarding school affiliated with the Church of Ireland in Dublin, Ireland * St Columba's College, Essendon, an all-female Catholic secondary school in Melbourne, Australia * St Columba's College, St Albans, a Catholic independent boys' school in St Albans, England * St. Columba's High School (disambiguation), multiple schools * St Columba's Roman Catholic High School, Dunfermline in Scotland * St. Columba's School, Delhi, India * St Columba's School, Kilmacolm, Scotland * St Columba's High School, Gourock, Scotland Other * Cathach of St. Columba, an early seventh-century Irish Psalter * Knights of St Columba, a Scottish Order of Catholic Laymen * Urney St. Columba's GAC, a Gaelic Athletic Association club in County Tyrone, Northern Ireland * St. Kolumba, Cologne, a destroyed church in Cologne, Germany, now chapel * MS Masarrah, a ferry originally named St. Columba, working on the Irish sea See also * Columba (disambiguation) * Columbanus (540–615), also known as St. Columban, was an Irish missionary * Santa Coloma (disambiguation) * St Columb (disambiguation) * St. Columba's Church (disambiguation) "

❤️ Spontaneous emission ✨

"Spontaneous emission is the process in which a quantum mechanical system (such as a molecule, an atom or a subatomic particle) transits from an excited energy state to a lower energy state (e.g., its ground state) and emits a quantized amount of energy in the form of a photon. Spontaneous emission is ultimately responsible for most of the light we see all around us; it is so ubiquitous that there are many names given to what is essentially the same process. If atoms (or molecules) are excited by some means other than heating, the spontaneous emission is called luminescence. For example, fireflies are luminescent. And there are different forms of luminescence depending on how excited atoms are produced (electroluminescence, chemiluminescence etc.). If the excitation is affected by the absorption of radiation the spontaneous emission is called fluorescence. Sometimes molecules have a metastable level and continue to fluoresce long after the exciting radiation is turned off; this is called phosphorescence. Figurines that glow in the dark are phosphorescent. Lasers start via spontaneous emission, then during continuous operation work by stimulated emission. Spontaneous emission cannot be explained by classical electromagnetic theory and is fundamentally a quantum process. The first person to derive the rate of spontaneous emission accurately from first principles was Dirac in his quantum theory of radiation, the precursor to the theory which he later called quantum electrodynamics. Contemporary physicists, when asked to give a physical explanation for spontaneous emission, generally invoke the zero-point energy of the electromagnetic field. In 1963, the Jaynes–Cummings model was developed describing the system of a two-level atom interacting with a quantized field mode (i.e. the vacuum) within an optical cavity. It gave the nonintuitive prediction that the rate of spontaneous emission could be controlled depending on the boundary conditions of the surrounding vacuum field. These experiments gave rise to cavity quantum electrodynamics (CQED), the study of effects of mirrors and cavities on radiative corrections. Introduction If a light source ('the atom') is in an excited state with energy E_2, it may spontaneously decay to a lower lying level (e.g., the ground state) with energy E_1, releasing the difference in energy between the two states as a photon. The photon will have angular frequency \omega and an energy \hbar \omega: :E_2 - E_1 = \hbar \omega, where \hbar is the reduced Planck constant. Note: \hbar \omega = h u, where h is the Planck constant and u is the linear frequency. The phase of the photon in spontaneous emission is random as is the direction in which the photon propagates. This is not true for stimulated emission. An energy level diagram illustrating the process of spontaneous emission is shown below: Image:Spontaneousemission.png If the number of light sources in the excited state at time t is given by N(t), the rate at which N decays is: :\frac{\partial N(t)}{\partial t} = -A_{21} N(t), where A_{21} is the rate of spontaneous emission. In the rate-equation A_{21} is a proportionality constant for this particular transition in this particular light source. The constant is referred to as the Einstein A coefficient, and has units s^{-1}.R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University Press Inc., New York, 2001). The above equation can be solved to give: :N(t) =N(0) e^{ - A_{21}t }= N(0) e^{ - \Gamma_{\text{rad}}t }, where N(0) is the initial number of light sources in the excited state, t is the time and \Gamma_{\text{rad}} is the radiative decay rate of the transition. The number of excited states N thus decays exponentially with time, similar to radioactive decay. After one lifetime, the number of excited states decays to 36.8% of its original value (\frac{1}{e}-time). The radiative decay rate \Gamma_{\text{rad}} is inversely proportional to the lifetime \tau_{21}: :A_{21}=\Gamma_{21}=\frac{1}{\tau_{21}}. Theory Spontaneous transitions were not explainable within the framework of the Schrödinger equation, in which the electronic energy levels were quantized, but the electromagnetic field was not. Given that the eigenstates of an atom are properly diagonalized, the overlap of the wavefunctions between the excited state and the ground state of the atom is zero. Thus, in the absence of a quantized electromagnetic field, the excited state atom cannot decay to the ground state. In order to explain spontaneous transitions, quantum mechanics must be extended to a quantum field theory, wherein the electromagnetic field is quantized at every point in space. The quantum field theory of electrons and electromagnetic fields is known as quantum electrodynamics. In quantum electrodynamics (or QED), the electromagnetic field has a ground state, the QED vacuum, which can mix with the excited stationary states of the atom. As a result of this interaction, the "stationary state" of the atom is no longer a true eigenstate of the combined system of the atom plus electromagnetic field. In particular, the electron transition from the excited state to the electronic ground state mixes with the transition of the electromagnetic field from the ground state to an excited state, a field state with one photon in it. Spontaneous emission in free space depends upon vacuum fluctuations to get started. Although there is only one electronic transition from the excited state to ground state, there are many ways in which the electromagnetic field may go from the ground state to a one-photon state. That is, the electromagnetic field has infinitely more degrees of freedom, corresponding to the different directions in which the photon can be emitted. Equivalently, one might say that the phase space offered by the electromagnetic field is infinitely larger than that offered by the atom. This infinite degree of freedom for the emission of the photon results in the apparent irreversible decay, i.e., spontaneous emission. In the presence of electromagnetic vacuum modes, the combined atom-vacuum system is explained by the superposition of the wavefunctions of the excited state atom with no photon and the ground state atom with a single emitted photon: : \psi(t)\rangle = a(t)e^{-i\omega_0 t}e;0\rangle + \sum_{k,s} b_{ks}(t)e^{-i\omega_k t}g;1_{ks}\rangle where e;0\rangle and a(t) are the atomic excited state-electromagnetic vacuum wavefunction and its probability amplitude, g;1_{ks}\rangle and b_{ks}(t) are the ground state atom with a single photon (of mode ks ) wavefunction and its probability amplitude, \omega_0 is the atomic transition frequency, and \omega_k = ck is the frequency of the photon. The sum is over k and s , which are the wavenumber and polarization of the emitted photon, respectively. As mentioned above, the emitted photon has a chance to be emitted with different wavenumbers and polarizations, and the resulting wavefunction is a superposition of these possibilities. To calculate the probability of the atom at the ground state ( b(t)^2), one needs to solve the time evolution of the wavefunction with an appropriate Hamiltonian. To solve for the transition amplitude, one needs to average over (integrate over) all the vacuum modes, since one must consider the probabilities that the emitted photon occupies various parts of phase space equally. The "spontaneously" emitted photon has infinite different modes to propagate into, thus the probability of the atom re-absorbing the photon and returning to the original state is negligible, making the atomic decay practically irreversible. Such irreversible time evolution of the atom-vacuum system is responsible for the apparent spontaneous decay of an excited atom. If one were to keep track of all the vacuum modes, the combined atom-vacuum system would undergo unitary time evolution, making the decay process reversible. Cavity quantum electrodynamics is one such system where the vacuum modes are modified resulting in the reversible decay process, see also Quantum revival. The theory of the spontaneous emission under the QED framework was first calculated by Weisskopf and Wigner. In spectroscopy one can frequently find that atoms or molecules in the excited states dissipate their energy in the absence of any external source of photons. This is not spontaneous emission, but is actually nonradiative relaxation of the atoms or molecules caused by the fluctuation of the surrounding molecules present inside the bulk. Rate of spontaneous emission The rate of spontaneous emission (i.e., the radiative rate) can be described by Fermi's golden rule.B. Henderson and G. Imbusch, Optical Spectroscopy of Inorganic Solids (Clarendon Press, Oxford, UK, 1989). The rate of emission depends on two factors: an 'atomic part', which describes the internal structure of the light source and a 'field part', which describes the density of electromagnetic modes of the environment. The atomic part describes the strength of a transition between two states in terms of transition moments. In a homogeneous medium, such as free space, the rate of spontaneous emission in the dipole approximation is given by: : \Gamma_{\text{rad}}(\omega)= \frac{\omega^3n\mu_{12}^2} {3\pi\varepsilon_{0}\hbar c^3} = \frac{4 \alpha \omega^3n \langle 1\mathbf{r}2\rangle ^2} {3 c^2} : \frac{\mu_{12}^2} {\pi\varepsilon_{0}\hbar c} = 4 \alpha \langle 1\mathbf{r}2\rangle ^2 where \omega is the emission frequency, n is the index of refraction, \mu_{12} is the transition dipole moment, \varepsilon_0 is the vacuum permittivity, \hbar is the reduced Planck constant, c is the vacuum speed of light, and \alpha is the fine structure constant. The expression \langle 1\mathbf{r}2\rangle stands for the definition of the transition dipole moment \mu_{12}=\langle 1\mathbf{d}2\rangle for dipole moment operator \mathbf{d}=q\mathbf{r}, where q is the elementary charge and \mathbf{r} stands for position operator. (This approximation breaks down in the case of inner shell electrons in high-Z atoms.) The above equation clearly shows that the rate of spontaneous emission in free space increases proportionally to \omega^3. In contrast with atoms, which have a discrete emission spectrum, quantum dots can be tuned continuously by changing their size. This property has been used to check the \omega^3-frequency dependence of the spontaneous emission rate as described by Fermi's golden rule.A. F. van Driel, G. Allan, C. Delerue, P. Lodahl,W. L. Vos and D. Vanmaekelbergh, Frequency-dependent spontaneous emission rate from CdSe and CdTe nanocrystals: Influence of dark states, Physical Review Letters, 95, 236804 (2005).http://cops.tnw.utwente.nl/pdf/05/PHYSICAL%20REVIEW%20LETTERS%2095%20236804%20(2005).pdf Radiative and nonradiative decay: the quantum efficiency In the rate- equation above, it is assumed that decay of the number of excited states N only occurs under emission of light. In this case one speaks of full radiative decay and this means that the quantum efficiency is 100%. Besides radiative decay, which occurs under the emission of light, there is a second decay mechanism; nonradiative decay. To determine the total decay rate \Gamma_{\text{tot}}, radiative and nonradiative rates should be summed: :\Gamma_{\text{tot}}=\Gamma_{\text{rad}} + \Gamma_{\text{nrad}} where \Gamma_{\text{tot}} is the total decay rate, \Gamma_{\text{rad}} is the radiative decay rate and \Gamma_{\text{nrad}} the nonradiative decay rate. The quantum efficiency (QE) is defined as the fraction of emission processes in which emission of light is involved: : QE=\frac{\Gamma_{\text{rad}}}{\Gamma_{\text{nrad}} + \Gamma_{\text{rad}}}. In nonradiative relaxation, the energy is released as phonons, more commonly known as heat. Nonradiative relaxation occurs when the energy difference between the levels is very small, and these typically occur on a much faster time scale than radiative transitions. For many materials (for instance, semiconductors), electrons move quickly from a high energy level to a meta- stable level via small nonradiative transitions and then make the final move down to the bottom level via an optical or radiative transition. This final transition is the transition over the bandgap in semiconductors. Large nonradiative transitions do not occur frequently because the crystal structure generally cannot support large vibrations without destroying bonds (which generally doesn't happen for relaxation). Meta-stable states form a very important feature that is exploited in the construction of lasers. Specifically, since electrons decay slowly from them, they can be deliberately piled up in this state without too much loss and then stimulated emission can be used to boost an optical signal. See also * Absorption (optics) * Stimulated emission * Emission spectrum * Spectral line * Atomic spectral line * Laser science * Purcell effect * Photonic crystal * Vacuum Rabi oscillation * Jaynes–Cummings model References External links * Detail calculation of the Spontaneous Emission: Weisskopf-Wigner Theory * Britney's Guide to Semiconductor Physics Category:Concepts in physics Category:Laser science Category:Electromagnetic radiation Category:Charge carriers "

❤️ Nicolas Léonard Sadi Carnot ✨

"Sous-lieutenant Nicolas Léonard Sadi Carnot (; 1 June 1796 – 24 August 1832) was a French mechanical engineer in the French Army, military scientist and physicist, often described as the "father of thermodynamics." Like Copernicus, he published only one book, the Reflections on the Motive Power of Fire (Paris, 1824), in which he expressed, at the age of 27 years, the first successful theory of the maximum efficiency of heat engines. In this work he laid the foundations of an entirely new discipline, thermodynamics. Carnot's work attracted little attention during his lifetime, but it was later used by Rudolf Clausius and Lord Kelvin to formalize the second law of thermodynamics and define the concept of entropy. His father used the suffix Sadi to name him because of his intense interest in the character of Saadi Shirazi, a well- known Iranian poet. Life Nicolas Léonard Sadi Carnot was born in Paris into a family that was distinguished in both science and politics. He was the first son of Lazare Carnot, an eminent mathematician, military engineer and leader of the French Revolutionary Army. Lazare chose his son's third given name (by which he would always be known) after the Persian poet Sadi of Shiraz. Sadi was the elder brother of statesman Hippolyte Carnot and the uncle of Marie François Sadi Carnot, who would serve as President of France from 1887 to 1894. At the age of 16, Sadi Carnot became a cadet in the École Polytechnique in Paris, where his classmates included Michel Chasles and Gaspard-Gustave Coriolis. The École Polytechnique was intended to train engineers for military service, but its professors included such eminent scientists as André-Marie Ampère, François Arago, Joseph Louis Gay-Lussac, Louis Jacques Thénard and Siméon Denis Poisson, and the school had become renowned for its mathematical instruction. After graduating in 1814, Sadi became an officer in the French army's corps of engineers. His father Lazare had served as Napoleon's minister of the interior during the "Hundred Days", and after Napoleon's final defeat in 1815 Lazare was forced into exile. Sadi's position in the army, under the restored Bourbon monarchy of Louis XVIII, became increasingly difficult.Sadi Carnot et l’essor de la thermodynamique, CNRS Éditions Sadi Carnot was posted to different locations, he inspected fortifications, tracked plans and wrote many reports. It appears his recommendations were ignored and his career was stagnating. On 15 September 1818 he took a six-month leave to prepare for the entrance examination of Royal Corps of Staff and School of Application for the Service of the General Staff. In 1819, Sadi transferred to the newly formed General Staff, in Paris. He remained on call for military duty, but from then on he dedicated most of his attention to private intellectual pursuits and received only two-thirds pay. Carnot befriended the scientist Nicolas Clément and attended lectures on physics and chemistry. He became interested in understanding the limitation to improving the performance of steam engines, which led him to the investigations that became his Reflections on the Motive Power of Fire, published in 1824. Carnot retired from the army in 1828, without a pension. He was interned in a private asylum in 1832 as suffering from "mania" and "general delirum", and he died of cholera shortly thereafter, aged 36, at the hospital in Ivry-sur-Seine. Reflections on the Motive Power of Fire =Background= When Carnot began working on his book, steam engines had achieved widely recognized economic and industrial importance, but there had been no real scientific study of them. Newcomen had invented the first piston- operated steam engine over a century before, in 1712; some 50 years after that, James Watt made his celebrated improvements, which were responsible for greatly increasing the efficiency and practicality of steam engines. Compound engines (engines with more than one stage of expansion) had already been invented, and there was even a crude form of internal-combustion engine, with which Carnot was familiar and which he described in some detail in his book. Although there existed some intuitive understanding of the workings of engines, scientific theory for their operation was almost nonexistent. In 1824 the principle of conservation of energy was still poorly developed and controversial, and an exact formulation of the first law of thermodynamics was still more than a decade away; the mechanical equivalence of heat would not be formulated for another two decades. The prevalent theory of heat was the caloric theory, which regarded heat as a sort of weightless and invisible fluid that flowed when out of equilibrium. Engineers in Carnot's time had tried, by means such as highly pressurized steam and the use of fluids, to improve the efficiency of engines. In these early stages of engine development, the efficiency of a typical engine--the useful work it was able to do when a given quantity of fuel was burned--was only 3%. =Carnot cycle= Carnot wanted to answer two questions about the operation of heat engines: "Is the work available from a heat source potentially unbounded?" and "Can heat engines in principle be improved by replacing the steam with some other working fluid or gas?" He attempted to answer these in a memoir, published as a popular work in 1824 when he was only 27 years old. It was entitled Réflexions sur la Puissance Motrice du Feu ("Reflections on the Motive Power of Fire"). The book was plainly intended to cover a rather wide range of topics about heat engines in a rather popular fashion; equations were kept to a minimum and called for little more than simple algebra and arithmetic, except occasionally in the footnotes, where he indulged in a few arguments involving some calculus. He discussed the relative merits of air and steam as working fluids, the merits of various aspects of steam engine design, and even included some ideas of his own regarding possible practical improvements. The most important part of the book was devoted to an abstract presentation of an idealized engine that could be used to understand and clarify the fundamental principles that are generally applied to all heat engines, independent of their design. Perhaps the most important contribution Carnot made to thermodynamics was his abstraction of the essential features of the steam engine, as they were known in his day, into a more general and idealized heat engine. This resulted in a model thermodynamic system upon which exact calculations could be made, and avoided the complications introduced by many of the crude features of the contemporary steam engine. By idealizing the engine, he could arrive at clear and indisputable answers to his original two questions. He showed that the efficiency of this idealized engine is a function only of the two temperatures of the reservoirs between which it operates. He did not, however, give the exact form of the function, which was later shown to be (T1−T2)/T1, where T1 is the absolute temperature of the hotter reservoir. (Note: This equation probably came from Kelvin.) No thermal engine operating any other cycle can be more efficient, given the same operating temperatures. The Carnot cycle is the most efficient possible engine, not only because of the (trivial) absence of friction and other incidental wasteful processes; the main reason is that it assumes no conduction of heat between parts of the engine at different temperatures. Carnot knew that the conduction of heat between bodies at different temperatures is a wasteful and irreversible process, which must be eliminated if the heat engine is to achieve maximum efficiency. Regarding the second point, he also was quite certain that the maximum efficiency attainable did not depend upon the exact nature of the working fluid. He stated this for emphasis as a general proposition: For his "motive power of heat", we would today say "the efficiency of a reversible heat engine", and rather than "transfer of caloric" we would say "the reversible transfer of entropy ∆S" or "the reversible transfer of heat at a given temperature Q/T". He knew intuitively that his engine would have the maximum efficiency, but was unable to state what that efficiency would be. He concluded: and In an idealized model, the caloric transported from a hot to a cold body by a frictionless heat engine that lacks of conductive heat flow, driven by a difference of temperature, yielding work, could also be used to transport the caloric back to the hot body by reversing the motion of the engine consuming the same amount of work, a concept subsequently known as thermodynamic reversibility. Carnot further postulated that no caloric is lost during the operation of his idealized engine. The process being completely reversible, executed by this kind of heat engine is the most efficient possible process. The assumption that heat conduction driven by a temperature difference cannot exist, so that no caloric is lost by the engine, guided him to design the Carnot-cycle to be operated by his idealized engine. The cycle is consequently composed of adiabatic processes where no heat/caloric ∆S = 0 flows and isothermal processes where heat is transferred ∆S > 0 but no temperature difference ∆T = 0 exist. The proof of the existence of a maximum efficiency for heat engines is as follows: As the cycle named after him doesn't waste caloric, the reversible engine has to use this cycle. Imagine now two large bodies, a hot and a cold one. He postulates now the existence of a heat machine with a greater efficiency. We couple now two idealized machine but of different efficiencies and connect them to the same hot and the same cold body. The first and less efficient one lets a constant amount of entropy ∆S = Q/T flow from hot to cold during each cycle, yielding an amount of work denoted W. If we use now this work to power the other more efficient machine, it would, using the amount of work W gained during each cycle by the first machine, make an amount of entropy ∆S' > ∆S flow from the cold to the hot body. The net effect is a flow of ∆S' − ∆S ≠ 0 of entropy from the cold to the hot body, while no net work is done. Consequently, the cold body is cooled down and the hot body rises in temperature. As the difference of temperature rises now the yielding of work by the first is greater in the successive cycles and due to the second engine difference in temperature of the two bodies stretches by each cycle even more. In the end this set of machines would be a perpetuum mobile that cannot exist. This proves that the assumption of the existence of a more efficient engine was wrong so that an heat engine that operates the Carnot cycle must be the most efficient one. This means that a frictionless heat engine that lacks of conductive heat flow driven by a difference of temperature shows maximum possible efficiency. He concludes further that the choice of the working fluid, its density or the volume occupied by it cannot change this maximum efficiency. Using the equivalence of any working gas used in heat engines he deduced that the difference in the specific heat of a gas measured at constant pressure and at constant volume must be constant for all gases. By comparing the operation of his hypothetical heat engines for two different volumes occupied by the same amount of working gas he correctly deduces the relation between entropy and volume for an isothermal process: \Delta S \propto \ln \frac{V}{V_0}. Reception and later life Carnot's book received very little attention from his contemporaries. The only reference to it within a few years after its publication was in a review in the periodical Revue Encyclopédique, which was a journal that covered a wide range of topics in literature. The impact of the work had only become apparent once it was modernized by Émile Clapeyron in 1834 and then further elaborated upon by Clausius and Kelvin, who together derived from it the concept of entropy and the second law of thermodynamics. On Carnot's religious views, he was a Philosophical theist. As a deist, he believed in divine causality, stating that "what to an ignorant man is chance, cannot be chance to one better instructed," but he did not believe in divine punishment. He criticized established religion, though at the same time spoke in favor of "the belief in an all-powerful Being, who loves us and watches over us."R. H. Thurston, 1890., Appendix A. pp. 215–217 He was a reader of Blaise Pascal, Molière and Jean de La Fontaine.R. H. Thurston, 1890, p. 28 Death Carnot died during a cholera epidemic in 1832, at the age of 36. Because of the contagious nature of cholera, many of Carnot's belongings and writings were buried together with him after his death. As a consequence, only a handful of his scientific writings survived. After the publication of Reflections on the Motive Power of Fire, the book quickly went out of print and for some time was very difficult to obtain. Kelvin, for one, had a difficult time getting a copy of Carnot's book. In 1890 an English translation of the book was published by R. H. Thurston; this version has been reprinted in recent decades by Dover and by Peter Smith, most recently by Dover in 2005. Some of Carnot's posthumous manuscripts have also been translated into English. Carnot published his book in the heyday of steam engines. His theory explained why steam engines using superheated steam were better because of the higher temperature of the consequent hot reservoir. Carnot's theories and efforts did not immediately help improve the efficiency of steam engines; his theories only helped to explain why one existing practice was superior to others. It was only towards the end of the nineteenth century that Carnot's ideas, namely that a heat engine can be made more efficient if the temperature of its hot reservoir is increased, were put into practice. Carnot's book did, however, eventually have a real impact on the design of practical engines. Rudolf Diesel, for example, used Carnot's theories to design the diesel engine, in which the temperature of the hot reservoir is much higher than that of a steam engine, resulting in an engine which is more efficient. See also * History of the internal combustion engine Works * Reflections on the Motive Power of Fire (1824) References Bibliography * (full text of 1897 ed.) () * External links Reflections on the Motive Power of Heat (1890), English translation by R. H. Thurston (at Internet Archive) * Sadi Carnot and the Second Law of Thermodynamics, J. Srinivasan, Resonance, November 2001, 42 (PDF file) * Reflections on the Motive Power of Heat (1824), analysed on BibNum (click "À télécharger" for English analysis) Category:1796 births Category:1832 deaths Category:19th-century French mathematicians Category:French deists Category:École Polytechnique alumni Category:French military engineers Category:French scientists Category:Thermodynamicists Category:Deaths from cholera Category:Infectious disease deaths in France Category:People from Paris Category:Fluid dynamicists Category:Carnot family Category:Conservatoire national des arts et métiers alumni "