2,896 research outputs found
A general formal memory framework in Coq for verifying the properties of programs based on higher-order logic theorem proving with increased automation, consistency, and reusability
In recent years, a number of lightweight programs have been deployed in
critical domains, such as in smart contracts based on blockchain technology.
Therefore, the security and reliability of such programs should be guaranteed
by the most credible technology. Higher-order logic theorem proving is one of
the most reliable technologies for verifying the properties of programs.
However, programs may be developed by different high-level programming
languages, and a general, extensible, and reusable formal memory (GERM)
framework that can simultaneously support different formal verification
specifications, particularly at the code level, is presently unavailable for
verifying the properties of programs. Therefore, the present work proposes a
GERM framework to fill this gap. The framework simulates physical memory
hardware structure, including a low-level formal memory space, and provides a
set of simple, nonintrusive application programming interfaces and assistant
tools using Coq that can support different formal verification specifications
simultaneously. The proposed GERM framework is independent and customizable,
and was verified entirely in Coq. We also present an extension of Curry-Howard
isomorphism, denoted as execution-verification isomorphism (EVI), which
combines symbolic execution and theorem proving for increasing the degree of
automation in higher-order logic theorem proving assistant tools. We also
implement a toy functional programming language in a generalized algebraic
datatypes style and a formal interpreter in Coq based on the GERM framework.
These implementations are then employed to demonstrate the application of EVI
to a simple code segment.Comment: 27 pages, 28 figure
Effects of counterrotating interaction on driven tunneling dynamics: coherent destruction of tunneling and Bloch-Siegert shift
We investigate the dynamics of a driven two-level system (classical Rabi
model) using the counter-rotating-hybridized rotating wave method (CHRW), which
is a simple method based on a unitary transformation with a parameter .
This approach is beyond the traditional rotating-wave approximation (Rabi-RWA)
and more importantly, remains the RWA form with a renormalized tunneling
strength and a modified driving strength. The reformulated rotating wave method
not only possesses the same mathematical simplicity as the Rabi-RWA but also
allows us to explore the effects of counter-rotating (CR) components. We focus
on the properties of off-resonance cases for which the Rabi-RWA method breaks
down. After comparing the results of different RWA schemes and those of the
numerically exact method in a wide range of parameter regime, we show that the
CHRW method gives the accurate driven dynamics which is in good agreement with
the numerical method. Moreover, the other RWA methods appear as various
limiting cases of the CHRW method. The CHRW method reveals the effects of the
CR terms clearly by means of coherent destruction of tunneling and
Bloch-Siegert shift. Our main results are as follows: (i) the dynamics of the
coherent destruction of tunneling is explicitly given and its dependence on
is clarified, which is quantitatively in good agreement with the exact
results; (ii) the CR modulated Rabi frequency and the Bloch-Siegert shift are
analytically calculated, which is the same as the exact results up to fourth
order; (iii) the validity of parameter regions of different RWA methods are
given and the comparison of dynamics of these methods are shown. Since the CHRW
approach is mathematically simple as well as tractable and physically clear, it
may be extended to some complicated problems where it is difficult to do a
numerical study.Comment: 28pages,6 figures. arXiv admin note: text overlap with
arXiv:1602.0441
Effect of bath temperature on the quantum decoherence
The dynamics of a qubit in two different environments are investigated
theoretically. The first environment is a two level system coupled to a bosonic
bath. And the second one is a damped harmonic oscillator. Based on a unitary
transformation, we find that the decoherence of the qubit can be reduced with
increasing temperature in the first case, which agree with the results in
[Phys. Rev. Lett. 100, 120401], whereas, it can not be reduced with in the
second case. In both cases, the qubit dynamics are changed substantially as the
coupling increases or finite detuning appears.Comment: 10 pages, 5 figure
Quantum critical point of spin-boson model and infrared catastrophe in bosonic bath
An analytic ground state is proposed for the unbiased spin-boson Hamiltonian,
which is non-Gaussian and beyond the Silbey-Harris ground state with lower
ground state energy. The infrared catastrophe in Ohmic and sub-Ohmic bosonic
bath plays an important role in determining the degeneracy of the ground state.
We show that the infrared divergence associated with the displacement of the
nonadiabatic modes in bath may be removed from the proposed ground state for
the coupling . Then is the quantum critical point
of a transition from non-degenerate to degenerate ground state and our
calculated agrees with previous numerical results.Comment: 11 pages, 2 figure
FEther: An Extensible Definitional Interpreter for Smart-contract Verifications in Coq
Blockchain technology adds records to a list using cryptographic links.
Therefore, the security of blockchain smart contracts is among the most popular
contemporary research topics. To improve the theorem-proving technology in this
field, we are developing an extensible hybrid verification tool chain, denoted
as FSPVM-E, for Ethereum smart contract verification. This hybrid system
extends the proof assistants in Coq, a formal proof-management system.
Combining symbolic execution with higher-order theorem-proving, it solves
consistency, automation, and reusability problems by standard theorem-proving
approaches. This article completes the FSPVM-E by developing its proof engine.
FSPVM-E is an extensible definitional interpreter based on our previous work
FEther, which is totally developed in the Coq proof assistant. It supports
almost all semantics of the Solidity programing language, and simultaneously
executes multiple types of symbols. FEther also contains a set of automatic
strategies that execute and verify the smart contracts in Coq with a high level
of automation. The functional correctness of FEther was verified in Coq. In
standard tutorials, the execution efficiency of FEther far exceeded that of the
interpreters developed in Coq.Comment: 33 pages, 18 figures, 8 table
Bloch-Siegert shift of the Rabi model
We apply a simple analytical method based on a unitary transformation to
calculate the Bloch-Siegert (BS) shift over the entire driving-strength range.
In quantitative comparison with the numerically exact BS shift obtained by
Floquet formalism as well as the previous BS results, we confirm that our
calculated results are not only accurate in the weak-driving regime but also
correct in strong-driving limit. In the intermediate strong-driving regime, the
calculated values of the BS shift are nearly the same as the exact ones. It
turns out that our calculation for the BS shift is beyond perturbation.
Meanwhile, we demonstrate the signatures caused by the BS shift by monitoring
the excited-state population and the probe-pump spectrum under the experiment
accessible conditions. In particular, we find that when the driving frequency
is fixed at the transition frequency of the system, the lineshape of the
probe-pump spectrum becomes asymmetric with the increase of the driving
strength, which may be verified experimentally.Comment: 5 figure
Topology-Induced Symmetry Breaking for Vortex with Artificial Monopole
We construct an artificial U(1) gauge field in the cold atom system to form a
monopole along with vortices. It is supposed that the cold atoms are confined
on a spherical surface, and two sets of identical laser beams in the opposite
propagating directions shine on two sides of the sphere. Arbitrary Chern number
CN, proportional to the quantized magnetic flux, can be obtained by selecting
proper laser modes. This construction meets the condition of Chern's theorem,
so that the vortices of the atom wave function will emerge on the sphere, whose
winding number equals CN. It is found that a geometric symmetry is broken
spontaneously for odd CN, which corresponds to a topology-induced quantum phase
transition. In particular for CN=1, the ground state of the cold atoms are
double-degenerate and can be applied to make a stable qubit. Since the
ground-state degeneracy is protected by topology-induced symmetry breaking
against dissipation, the proposed topological structure has vast potential in
quantum storage
An ansatz to the quantum phase transition in a dissipative two-qubit system
By means of a unitary transformation, we propose an ansatz to study quantum
phase transitions in the ground state of a two-qubit system interacting with a
dissipative reservoir. First, the ground state phase diagram is analyzed in the
presence of the Ohmic and sub-Ohmic bath using an analytic ground state wave
function which takes into account the competition between intrasite tunneling
and intersite correlation. The quantum critical point is determined as the
transition point from non-degenerate to degenerate ground state and our
calculated critical coupling strength agrees with that from the
numerical renormalization group method. Moreover, by computing the entanglement
entropy between the qubits and the bath as well as the qubit-qubit correlation
function in the ground state, we explore the nature of the quantum phase
transition between the delocalized and localized states.Comment: 20 pages, 10 figure
Resonance fluorescence of strongly driven two-level system coupled to multiple dissipative baths
We present a theoretical formalism for resonance fluorescence radiating from
a two-level system (TLS) driven by any periodic driving and coupled to multiple
reservoirs. The formalism is derived analytically based on the combination of
Floquet theory and Born-Markov master equation. The formalism allows us to
calculate the spectrum when the Floquet states and quasienergies are
analytically or numerically solved for simple or complicated driving fields. We
can systematically explore the spectral features by implementing the present
formalism. To exemplify this theory, we apply the unified formalism to
comprehensively study a generic model that a harmonically driven TLS is
simultaneously coupled to a radiative reservoir and a dephasing reservoir. We
demonstrate that the significant features of the fluorescence spectra, the
driving-induced asymmetry and the dephasing-induced asymmetry, can be
attributed to the violation of detailed balance condition, and explained in
terms of the driving-related transition quantities between Floquet-states and
their steady populations. In addition, we find the distinguished features of
the fluorescence spectra under the biharmonic and multiharmonic driving fields
in contrast with that of the harmonic driving case. In the case of the
biharmonic driving, we find that the spectra is significantly different from
the result of the rotating-wave approximation (RWA) under the multiple
resonance conditions. By the three concrete applications, we illustrate that
the present formalism provides a routine tool for comprehensively exploring the
fluorescence spectrum of periodically strongly driven TLSs.Comment: 22 pages, 13 figure
Protecting coherence by reservoir engineering: intense bath disturbance
We put forward a scheme based on reservoir engineering to protect quantum
coherence from leaking to bath, in which we intensely disturb the Lorentzian
bath by N harmonic oscillators. We show that the intense disturbance changes
the spectrum of the bath and reduces the qubit-bath interaction. Furthermore,
we give the exact time evolution with the Lorentzian spectrum by a master
equation, and calculate the concurrence and survival probability of the qubits
to demonstrate the effect of the intense bath disturbance on the protection of
coherence. Meanwhile, we reveal the dynamic effects of counter-rotating
interaction on the qubits as compared to the results of the rotating wave
approximation.Comment: 19 pages, 8 figures; Accepted by Quantum Inf. Proces
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