What is Ensemble: Definition and 125 Discussions

The Alexandrov Ensemble (Russian: Ансамбль Александрова, tr. Ansambl Aleksandrova; commonly known as the Red Army Choir in Western Europe) is an official army choir of the Russian armed forces. Founded during the Soviet era, the ensemble consists of a male choir, an orchestra, and a dance ensemble.
The Ensemble has entertained audiences both in Russia and throughout the world, performing a range of music including folk tunes, hymns, operatic arias and popular music. The group's repertoire has included The Volga Boatmen's Song, Katyusha, Kalinka, and Ave Maria.
It is named for its first director, Alexander Vasilyevich Alexandrov (1883–1946). Its formal name since 1998 has been A. V. Alexandrov Academic Song and Dance Ensemble of the Russian Army (Russian: Академи́ческий анса́мбль пе́сни и пля́ски Росси́йской А́рмии и́мени А. В. Алекса́ндрова, tr. Akademíchesky ansámbl′ pésni i plyáski Rossýskoy Ármii ímeni A. V. Aleksándrova), shortened to Academic Ensemble (Russian: Академи́ческий анса́мбль, tr. Akademíchesky ansámbl′) on second reference.
On 25 December 2016, its artistic director, Valery Khalilov, and 63 other members of the Ensemble were killed in the Russian Defence Ministry aircraft crash of a 1983 Tupolev Tu-154 into the Black Sea just after takeoff from the southern resort city of Sochi, Russia. The Red Army Choir singers and dancers were en route to Syria to entertain Russian troops there for Orthodox Christmas celebrations.

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  1. Morbert

    I Minimal vs Instrumental vs Ensemble

    I've recently had a look back at the review by Home and Whitaker as well as Asher Peres's book "Quantum Theory: Concepts and Methods". Both "minimal interpretation" and "ensemble interpretation" refer to categories of interpretations rather than interpretations themselves. Specifically, you can...
  2. cianfa72

    I Statistical ensemble in phase space

    Hi, I've a question about the concept of ensemble is statistical physics. Take a conservative system in a given macrostate (e.g. with a given energy): there will be a number of phase space's microstates compatible with the given macrostate. If I understand it correctly, basically the...
  3. E

    Ensemble vs. time averages and Ashcroft and Mermin Problem 1.1

    The question is as seen below: My attempt (note that my questions are in bold below) is below. Please note that I am self-studying AM: (a) By the independence of any interval ##dt## of time and time symmetry, we expect these two answers are the same (Is there any way to make this rigorous?)...
  4. G

    Canonical ensemble <(Delta E)^3> expression

    I try involving differentiating ^2 but I get an expression of different proportionality.
  5. Dario56

    I Concept of Thermal Equilibrium in the Context of Canonical Ensemble

    Canonical ensemble can be used to derive probability distribution for the internal energy of the closed system at constant volume ##V## and number of particles ##N## in thermal contact with the reservoir. Also, it is stated that the temperature of both system and reservoir is the same, i.e...
  6. Dario56

    I How Can Internal Energy of the Canonical Ensemble Change (Fluctuate)?

    Canonical ensemble is the statistical ensemble which is applicable for the closed system in contact with the reservoir at constant temperature ##T##. Canonical ensemble is characterized by the three fixed variables; number of particles ##N##, volume ##V## and temperature ##T##. What is said is...
  7. Dario56

    I Derivation of the Canonical Ensemble

    One of the common derivations of the canonical ensemble goes as follows: Assume there is a system of interest in the contact with heat reservoir which together form an isolated system. Heat can be exchanged between the system and reservoir until thermal equilibrium is established and both are...
  8. yucheng

    Derivation of Boltzmann Factor via Reservoir Method (canonical ensemble)

    https://scholar.harvard.edu/files/schwartz/files/7-ensembles.pdf https://mcgreevy.physics.ucsd.edu/s12/lecture-notes/chapter06.pdf On page 3 of both the notes above, the author merely claims that $$P \propto \Omega_{\text{reservoir}}$$ But isn't $$P \propto...
  9. Philip Koeck

    I Connecting the microcanonical with the (grand) canonical ensemble

    I'm trying to sort out how the microcanonical picture is connected to the canonical and the grand canonical. If I consider a Helium gas, not necessarily with low density, in an isolated container (fixed energy and particle number) I can use the microcanonical ensemble to arrive at the...
  10. bohm2

    A The wave-function as a true ensemble

    "We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all ψ-ensemble interpretations which reproduce quantum mechanics violate Statistical Independence." https://arxiv.org/abs/2109.02676
  11. Haorong Wu

    I Looking for materials about ensemble average

    Hello. I am looking for some materials related to the ensemble average. Specifically, suppose there is a function ##A(x)## satisfying a Gaussian white noise $$\left < A(x)A(x') \right > =A_0^2\exp \left ( -\frac 1 {L^2}(x-x')^2\right )$$ where the average is taken over an ensemble. Now I need...
  12. J

    A QM is Feynman path ensemble - is QFT Feynman field ensemble?

    While classical mechanics uses single action optimizing trajectory, QM can be formulated as Feynman ensemble of trajectories. As in derivation of Brownian motion, mathematically it is convenient to use nonphysical: nowhere differentiable trajectories - should it be so? Can this connection be...
  13. J

    I The Ensemble Interpretation and the Double Slit Experiment

    I am a big fan of Ballentine's book on QM and was reading the discussions about the Ensemble Interpretation. Although, I am not an expert on these matters I reject the idea of the wave function collapse as a fundamental postulate of QM. Instead, I've come to the conclusion that we don't...
  14. Demystifier

    A Is the Ensemble Interpretation Inconsistent with the PBR Theorem?

    [Moderator's note: Spun off from another thread due to topic and subforum change.] I think Ballentine's interpretation is ruled out by the PBR theorem. Maybe we could discuss that?
  15. J

    I Born rule in classical Ising model: Feynman -> Boltzmann ensemble?

    Quantum mechanics is often said to be equivalent with Feynman path ensemble, which "after Wick rotation" becomes Boltzmann path ensemble, also called euclidean path integrals (popular for numerical calculations), or random walk/diffusion MERW (maximal entropy random walk). But Boltzmann path...
  16. Mayan Fung

    Microcanonical ensemble generalized pressure

    In the discussion of the pressure in macrocanonical ensemble, I found in textbook that: ##dW = \bar p dV## (##dW## is in fact d_bar W, yet I can't type the bar) The derivation goes like: ##\bar p = \frac{1}{Z} \sum_{r} e^{-\beta E_r} (-\frac{\partial E_r}{\partial V}) = ... = \frac{1}{\beta}...
  17. T

    A special case of the grand canonical ensemble

    In addition to the homework statement and considering only the case where ##U= constant## and ##N = large## : Can we also consider the definition of chemical potential ##\mu## and temperature ##T## as in equations ##(1)## and ##(2)##, and use them in the grand partition function? More...
  18. L

    Why is the entropy calculated differently in the microcanonical ensemble?

    I have a problem to understand why this problem is microcanonical ensemble problem? And why entropy is calculated as S(E,N,V)=\ln \Gamma(E,N,V) When in microcanonical ensemble we spoke about energies between ##E## and ##E+\Delta E##.
  19. J

    Canonical ensemble and Force on the Walls of a box

    Hi everyone, this is my first message after presentation so please be merciful if the notation is somewhat messy. Here's my attempt at a solution: As for points 1) and 2) I used the definition of partition function $$Z = \frac{1}{h^{3N}} \int e^{-\beta \mathcal{H}} d^3p d^3q$$ and the fact that...
  20. C

    Phase space volume with a potential (microcanonical ensemble)

    I don't know how to solve that integral, and to calculate the number of microstates first, then aply convolution and then integrate to find the volume of the phase space seems to be more complicated. Any clue on how to solve this? Thank you very much.
  21. soothsayer

    I Questions about ensemble interpretation of QM

    I've been reading up on the ensemble interpretation (aka statistical interpretation) of QM and it's making a bit more sense to me that it did on the onset, but I still have some questions about how it is consistent with experimental observations of various QM experiments, especially...
  22. J

    A Liouville's theorem and time evolution of ensemble average

    With the Liouville's theorem $$\frac{{d\rho }}{{dt}} = \frac{{\partial \rho }}{{\partial t}} + \sum\limits_{a = 1}^{3N} {(\frac{{\partial \rho }}{{\partial {p_a}}}\frac{{d{p_a}}}{{dt}} + \frac{{\partial \rho }}{{\partial {q_a}}}\frac{{d{q_a}}}{{dt}})} = 0$$ when we calculate the time evolution...
  23. J

    I Relational Hidden Variables (Real ensemble or thermal?)

    Smolin latest book about the quantum is quite interesting. Its called "Einstein Unfinished Revolution: Search for What Lies Beyond the Quantum" and he has a new theory or interpretation. Id like to know what you make of it. The theory is very simple. Similar views produce QM. May i know how this...
  24. W

    I State functions in Grand Canonical Ensemble vs Canonical

    Hi all, I am slightly confused with regard to some ideas related to the GCE and CE. Assistance is greatly appreciated. Since the GCE's partition function is different from that of the CE's, are all state variables that are derived from the their respective partition functions still equal in...
  25. SchroedingersLion

    Pressure in canonical ensemble

    Greetings, I am having a hard time in understanding intuitively how pressure does not automatically stay constant in a canonical ensemble (=NVT ensemble). Pressure in a closed system is the average force of particles hitting against the wall of said system. The obvious way to manipulate...
  26. binbagsss

    SM:Parastatistics, grand canonical ensemble function

    Homework Statement Hi I am looking at the question attached. Parts c and d, see below Homework EquationsThe Attempt at a SolutionFirst of all showing that ##<N> ## and ##<n_r>## agree I have ##Z=\Pi_r z_r ##, where ##Z## here denotes the grand canonical ensemble. So therefore we have ##...
  27. binbagsss

    Statistical Mechanics-Limit in canonical ensemble

    Homework Statement question attached. My question is just about the size of the limit, how do you know whether to expand out the exponential or not (parts 2) and 4)) Homework Equations for small ##x## we can expand out ##e^{x} ## via taylor series. The Attempt at a Solution Solutions...
  28. zexxa

    Canonical ensemble of a simplified DNA representation

    Question Form the canoncial partition using the following conditions: 2 N-particles long strands can join each other at the i-th particle to form a double helix chain. Otherwise, the i-th particle of each strand can also be left unattached, leaving the chain "open" An "open" link gives the...
  29. E

    Statistical pressure for a canonical ensemble

    So the pressure for a canonical ensemble is: P = kbT dZ/dV P = pressure P = -∑pi dEi/dV Z = ∑e-βEi pi is the probability of being in microstate i Ei is the energy of state i β = 1/kbT <E> = U = average energy U = -1/Z dZ/dβ = -d(Ln(Z))/dβ How can the pressure (given above) be derived in...
  30. P

    B Quark/Gluon Ensemble In Hadron

    I know the PF rules regarding using only peer reviewed texts, but in this case, it's the only source I have access to and I'm not trying to promote the content in any way, really I'm just trying to understand if it is actually saying what it seems to be. https://arxiv.org/pdf/1303.3752...
  31. Pushoam

    Canonical Ensemble Homework: P(ε) & No. of Microstates with Energy (E-ε)

    Homework Statement The probability that the system has the energy ε i.e.P(ε). The system could have any energy between 0 and E. So, P(ε) = 1/(no. of possible systems with different energies) I cannot understand how P (ε) is related to the no. of possible microstates the reservior could have...
  32. D

    Entropy of ensemble of two level systems

    Homework Statement The fundamental equation of a system of \tidle{N} atoms each of which can exist an atomic state with energy e_u or in atomic state e_d (and in no other state) is F= - \tilde{N} k_B T \log ( e^{-\beta e_u} + e^{-\beta e_d} ) Here k_B is Boltzmann's constant \beta = 1/k_BT...
  33. G

    A Negative T for a spin 1 system in the canonical ensemble

    I'm interested in an apparent inconsistency with the result for negative temperatures for a spin 1 system of N particles. The partition function of such a system is \begin{equation} Z=(1+2\cosh(\beta \,\epsilon))^{N} \end{equation} where each particle can be in one of three energy states...
  34. Demystifier

    A Value of observable in statistical ensemble interpretation

    The statistical ensemble interpretation (SEI) is supposed to be a minimal interpretation of QM with the smallest amount of philosophy, vagueness and controversy. Yet it turns out not to be the case. For instance Ballentine, the inventor of SEI, interprets Bell theorem as a strong evidence of...
  35. digogalvao

    Proof of expectation value for a dynamic observable

    Homework Statement Show that: d<A(q,p)>/dt=<{A,H}>, where {A,H} is a Poisson Bracket Homework Equations Liouville theorem The Attempt at a Solution <A>=Tr(Aρ)⇒d<A>/dt=Tr(Adρ/dt)=Tr(A{H,ρ}) So, in order to get the correct result, Tr(A{H,ρ}) must be equal to Tr({A,H}ρ), but I don't think I can...
  36. G

    I Decomposing a density matrix of a mixed ensemble

    I'm trying to solve a problem where I am given a few matrices and asked to determine if they could be density matrices or not and if they are if they represent pure or mixed ensembles. In the case of mixed ensembles, I should find a decomposition in terms of a sum of pure ensembles. The matrix...
  37. L

    Energy fluctuations in canonical ensemble

    Homework Statement Consider an ensamble of particles that can be only in two states with the difference ##\delta## in energy, and take the ground state energy to be zero. Is it possible to find the particle in the excited state if ##k_BT=\delta/2##, i.e. if the thermal energy is lower than the...
  38. binbagsss

    Statistical Mechanics -- many copies of a canonical ensemble

    Homework Statement Hi I am looking at the attached extract from David Tong's lecure notes on statistical phsyics So we have a canonical ensemble system ##S##, and the idea is that we take ##W>>1## copies of the system ##S##, and the copies of ##W## taken together then can be treated as a...
  39. A. Neumaier

    I Exploring the Differences Between Virtual and Ordinary Statistical Ensembles

    Please translate to English, so that it can be discussed here! I am primarily interested in how the virtual ensemble differs from an ordinary statistical ensemble, i.e., a large collection of actually identically prepared systems. The latter is the usual ensemble on which one can make...
  40. binbagsss

    Plot Heat Capacity vs Temperature for a 2 state system microcananonical ensemble

    Homework Statement I have ##C= NK_B (\frac{\epsilon}{K_B T})^{2}e^{\frac{\epsilon}{K_B T}}\frac{1}{(e^{\frac{\epsilon}{K_BT}}+1)^2} ## and need to sketch ##C## vs. ##T## Homework Equations See above The Attempt at a Solution I have ##C= NK_B (\frac{\epsilon}{K_B...
  41. M

    Applying the grand canonical ensemble to a magnetic system

    Homework Statement Consider a system with N sites and N particles with magnetic moment m. Each site can be in one of three states: empty with energy 0, occupied by one particle with energy 0 (in the absent of magnetic field) or occupied by two particles with anti parallel moments and energy ε...
  42. ShayanJ

    A Measurement problem in the Ensemble interpretation

    The ensemble interpretation asserts that QM is only applicable to an ensemble of similarly prepared systems and has nothing to say about an individual system and in this way, it seems, it can prevent the need for introducing the concept of wave-function collapse and so it may seem that there is...
  43. bananabandana

    Understanding the Uniform Probability Distribution in Statistical Ensembles

    Homework Statement Confused about what a statistical ensemble actually means. Why does the ensemble have to have a uniform probability distribution at equilibrium? [If my definition of an ensemble is correct] The Attempt at a Solution This is what I understand so far: [/B] For any given...
  44. S

    I Query about statistical ensemble and Liouville's Theorem

    Hi, I was studying about the statistical ensemble theory and facing some problem to understand these concepts , I have understood that the ensemble is a collection of systems which are macroscopically identical but microscopically different . In some books they are called as systems with...
  45. A. Neumaier

    I Particles from a thermal source

    In the following, I want to consider both photons in a sharply focussed, monochromatic beam of light (''type P'') and electrons in an electron beam (''type E'') on the same footing. In the following, X is either P or E. If we only concentrate on the internal degrees of freedom, both kinds of...
  46. M

    How can energy vary in the canonical ensemble

    I must be missing some point with regards to the canonical Distribution. Let us imagine I have a closed (to energy and matter) box full of ideal gas at temperature T. The total energy in the box equals hence E=3N2kT , where N is the number of molecules, k Boltzmann's connstant.Next, I allow the...
  47. J

    Canonical Ensemble Microstates

    Hi, I've been looking at working with the canonical ensemble and getting the probabilities of a system being at a certain energy. For reference, I am following something of the form given under 'Canonical Ensemble' in this article...
  48. gre_abandon

    Demon algorithm for microcanonical ensemble

    I simulated a microcanonical ensemble of 10 ideal gas particles in one dimension and yielded the expected normal distribution of velocities. However, I still did not get how the algorithm works. The demon has non-negative energy content and the demon together with the system constitutes a closed...
  49. D

    Variation of system energy in Canonical Ensemble

    A system is in contact with a reservoir at a specific temperature. The macrostate of the system is specified by the triple (N,V,T) viz., particle number, volume and temperature. The canonical ensemble can be used to analyze the situation. In the canonical ensemble, the system can exchange...