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A branch of excitations for a 3-dimension system has a dispersion relation, ∈(k) = A k2/3 where, A is constant, ∈ is energy' and k is the magnitude of wave vector. The excitations are bosonic in nature and chemical potential is zero. The entropy(S) of the system varies on absolute temperature (T) as S ∝ Tn/2, the value of n is
Correct answer is '9'. Can you explain this answer?
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Which describes how the energy of the excitations depends on their momentum. In a 3-dimensional system, the dispersion relation may take different forms depending on the specific system under consideration.
For example, in a free particle system, the dispersion relation is given by the equation:
E^2 = p^2 + m^2
where E is the energy, p is the momentum, and m is the mass of the particle. This relation is derived from the relativistic energy-momentum equation.
In a crystal lattice, the dispersion relation can be more complex due to the periodic potential experienced by the particles. In this case, the dispersion relation is usually obtained by solving the Schrödinger equation for the system. The resulting relation may have multiple branches, corresponding to different types of excitations such as phonons (lattice vibrations) or electronic excitations.
The dispersion relation provides important information about the behavior of excitations in a system. It determines the allowed energy and momentum states of the excitations, and can reveal properties such as the speed of propagation, the presence of gaps or band structures, and the nature of the interactions between particles.
Overall, the dispersion relation is a fundamental concept in the study of excitations in 3-dimensional systems, and understanding it is crucial for understanding the behavior of particles and waves in various physical systems.
For example, in a free particle system, the dispersion relation is given by the equation:
E^2 = p^2 + m^2
where E is the energy, p is the momentum, and m is the mass of the particle. This relation is derived from the relativistic energy-momentum equation.
In a crystal lattice, the dispersion relation can be more complex due to the periodic potential experienced by the particles. In this case, the dispersion relation is usually obtained by solving the Schrödinger equation for the system. The resulting relation may have multiple branches, corresponding to different types of excitations such as phonons (lattice vibrations) or electronic excitations.
The dispersion relation provides important information about the behavior of excitations in a system. It determines the allowed energy and momentum states of the excitations, and can reveal properties such as the speed of propagation, the presence of gaps or band structures, and the nature of the interactions between particles.
Overall, the dispersion relation is a fundamental concept in the study of excitations in 3-dimensional systems, and understanding it is crucial for understanding the behavior of particles and waves in various physical systems.
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A branch of excitations for a 3-dimension system has a dispersion relation, ∈(k) = A k2/3 where, A is constant, ∈ is energy' and k is the magnitude of wave vector. The excitations are bosonic in nature and chemical potential is zero. The entropy(S) of the system varies on absolute temperature (T) as S ∝ Tn/2, the value of n isCorrect answer is '9'. Can you explain this answer?
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A branch of excitations for a 3-dimension system has a dispersion relation, ∈(k) = A k2/3 where, A is constant, ∈ is energy' and k is the magnitude of wave vector. The excitations are bosonic in nature and chemical potential is zero. The entropy(S) of the system varies on absolute temperature (T) as S ∝ Tn/2, the value of n isCorrect answer is '9'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A branch of excitations for a 3-dimension system has a dispersion relation, ∈(k) = A k2/3 where, A is constant, ∈ is energy' and k is the magnitude of wave vector. The excitations are bosonic in nature and chemical potential is zero. The entropy(S) of the system varies on absolute temperature (T) as S ∝ Tn/2, the value of n isCorrect answer is '9'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A branch of excitations for a 3-dimension system has a dispersion relation, ∈(k) = A k2/3 where, A is constant, ∈ is energy' and k is the magnitude of wave vector. The excitations are bosonic in nature and chemical potential is zero. The entropy(S) of the system varies on absolute temperature (T) as S ∝ Tn/2, the value of n isCorrect answer is '9'. Can you explain this answer?.
A branch of excitations for a 3-dimension system has a dispersion relation, ∈(k) = A k2/3 where, A is constant, ∈ is energy' and k is the magnitude of wave vector. The excitations are bosonic in nature and chemical potential is zero. The entropy(S) of the system varies on absolute temperature (T) as S ∝ Tn/2, the value of n isCorrect answer is '9'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A branch of excitations for a 3-dimension system has a dispersion relation, ∈(k) = A k2/3 where, A is constant, ∈ is energy' and k is the magnitude of wave vector. The excitations are bosonic in nature and chemical potential is zero. The entropy(S) of the system varies on absolute temperature (T) as S ∝ Tn/2, the value of n isCorrect answer is '9'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A branch of excitations for a 3-dimension system has a dispersion relation, ∈(k) = A k2/3 where, A is constant, ∈ is energy' and k is the magnitude of wave vector. The excitations are bosonic in nature and chemical potential is zero. The entropy(S) of the system varies on absolute temperature (T) as S ∝ Tn/2, the value of n isCorrect answer is '9'. Can you explain this answer?.
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